LMFDB - Embedded newform 25.5.f.a.12.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,Mod(2,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			12.9
Character	$\chi$	$=$	25.12
Dual form			25.5.f.a.23.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02122 + 6.44773i) q^{2} +(7.16973 + 3.65316i) q^{3} +(-25.3134 + 8.22483i) q^{4} +(24.6871 - 3.94298i) q^{5} +(-16.2327 + 49.9591i) q^{6} +(-53.8906 - 53.8906i) q^{7} +(-31.4629 - 61.7494i) q^{8} +(-9.55120 - 13.1461i) q^{9} +O(q^{10})$	\(q+(1.02122 + 6.44773i) q^{2} +(7.16973 + 3.65316i) q^{3} +(-25.3134 + 8.22483i) q^{4} +(24.6871 - 3.94298i) q^{5} +(-16.2327 + 49.9591i) q^{6} +(-53.8906 - 53.8906i) q^{7} +(-31.4629 - 61.7494i) q^{8} +(-9.55120 - 13.1461i) q^{9} +(50.6343 + 155.149i) q^{10} +(149.767 + 108.812i) q^{11} +(-211.537 - 33.5042i) q^{12} +(11.8912 - 75.0782i) q^{13} +(292.438 - 402.506i) q^{14} +(191.404 + 61.9158i) q^{15} +(21.4870 - 15.6112i) q^{16} +(67.7399 - 34.5152i) q^{17} +(75.0086 - 75.0086i) q^{18} +(21.7886 + 7.07953i) q^{19} +(-592.485 + 302.858i) q^{20} +(-189.510 - 583.252i) q^{21} +(-548.646 + 1076.78i) q^{22} +(-495.228 + 78.4364i) q^{23} -557.665i q^{24} +(593.906 - 194.682i) q^{25} +496.227 q^{26} +(-122.417 - 772.910i) q^{27} +(1807.40 + 920.915i) q^{28} +(-1041.95 + 338.551i) q^{29} +(-203.750 + 1297.35i) q^{30} +(-48.0298 + 147.821i) q^{31} +(-661.474 - 661.474i) q^{32} +(676.280 + 1327.28i) q^{33} +(291.722 + 401.521i) q^{34} +(-1542.89 - 1117.91i) q^{35} +(349.898 + 254.216i) q^{36} +(-253.383 - 40.1319i) q^{37} +(-23.3960 + 147.717i) q^{38} +(359.529 - 494.849i) q^{39} +(-1020.20 - 1400.36i) q^{40} +(2493.49 - 1811.63i) q^{41} +(3567.12 - 1817.54i) q^{42} +(-103.917 + 103.917i) q^{43} +(-4686.07 - 1522.60i) q^{44} +(-287.626 - 286.879i) q^{45} +(-1011.47 - 3113.00i) q^{46} +(-729.454 + 1431.63i) q^{47} +(211.086 - 33.4327i) q^{48} +3407.40i q^{49} +(1861.76 + 3630.53i) q^{50} +611.766 q^{51} +(316.498 + 1998.29i) q^{52} +(-2026.03 - 1032.31i) q^{53} +(4858.50 - 1578.62i) q^{54} +(4126.36 + 2095.73i) q^{55} +(-1632.16 + 5023.27i) q^{56} +(130.355 + 130.355i) q^{57} +(-3246.95 - 6372.49i) q^{58} +(3437.49 + 4731.30i) q^{59} +(-5354.34 + 6.96628i) q^{60} +(-1387.41 - 1008.01i) q^{61} +(-1002.16 - 158.726i) q^{62} +(-193.731 + 1223.17i) q^{63} +(3839.28 - 5284.31i) q^{64} +(-2.47245 - 1900.35i) q^{65} +(-7867.28 + 5715.91i) q^{66} +(-4164.25 + 2121.79i) q^{67} +(-1430.85 + 1430.85i) q^{68} +(-3837.19 - 1246.78i) q^{69} +(5632.37 - 11089.8i) q^{70} +(2518.85 + 7752.22i) q^{71} +(-511.256 + 1003.40i) q^{72} +(107.996 - 17.1049i) q^{73} -1674.73i q^{74} +(4969.34 + 773.817i) q^{75} -609.771 q^{76} +(-2207.09 - 13935.0i) q^{77} +(3557.81 + 1812.80i) q^{78} +(-3135.73 + 1018.86i) q^{79} +(468.897 - 470.118i) q^{80} +(1539.14 - 4736.97i) q^{81} +(14227.3 + 14227.3i) q^{82} +(-1746.99 - 3428.67i) q^{83} +(9594.30 + 13205.4i) q^{84} +(1536.21 - 1119.18i) q^{85} +(-776.148 - 563.905i) q^{86} +(-8707.30 - 1379.10i) q^{87} +(2006.98 - 12671.6i) q^{88} +(-1621.42 + 2231.69i) q^{89} +(1555.99 - 2147.50i) q^{90} +(-4686.83 + 3405.18i) q^{91} +(11890.8 - 6058.66i) q^{92} +(-884.373 + 884.373i) q^{93} +(-9975.72 - 3241.31i) q^{94} +(565.811 + 88.8612i) q^{95} +(-2326.12 - 7159.06i) q^{96} +(1210.96 - 2376.64i) q^{97} +(-21970.0 + 3479.71i) q^{98} -3008.14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.02122	+	6.44773i	0.255305	+	1.61193i	0.698570	+	0.715542i	$0.253820\pi$
$2$	1.02122	+	6.44773i	0.255305	+	1.61193i	−0.443265	+	0.896391i	$0.646180\pi$
$3$	7.16973	+	3.65316i	0.796636	+	0.405906i	0.804418	−	0.594063i	$-0.202477\pi$
$3$	7.16973	+	3.65316i	0.796636	+	0.405906i	−0.00778209	+	0.999970i	$0.502477\pi$
$4$	−25.3134	+	8.22483i	−1.58209	+	0.514052i
$5$	24.6871	−	3.94298i	0.987484	−	0.157719i
$5$	24.6871	−	3.94298i	0.987484	−	0.157719i
$6$	−16.2327	+	49.9591i	−0.450908	+	1.38775i
$7$	−53.8906	−	53.8906i	−1.09981	−	1.09981i	−0.994432	−	0.105377i	$-0.966395\pi$
$7$	−53.8906	−	53.8906i	−1.09981	−	1.09981i	−0.105377	−	0.994432i	$-0.533605\pi$
$8$	−31.4629	−	61.7494i	−0.491608	−	0.964835i
$9$	−9.55120	−	13.1461i	−0.117916	−	0.162297i
$10$	50.6343	+	155.149i	0.506343	+	1.55149i
$11$	149.767	+	108.812i	1.23774	+	0.899273i	0.997446	−	0.0714259i	$-0.0227549\pi$
$11$	149.767	+	108.812i	1.23774	+	0.899273i	0.240298	+	0.970699i	$0.422755\pi$
$12$	−211.537	−	33.5042i	−1.46901	−	0.232668i
$13$	11.8912	−	75.0782i	0.0703622	−	0.444249i	−0.927206	−	0.374552i	$-0.877797\pi$
$13$	11.8912	−	75.0782i	0.0703622	−	0.444249i	0.997568	−	0.0696976i	$-0.0222034\pi$
$14$	292.438	−	402.506i	1.49203	−	2.05360i
$15$	191.404	+	61.9158i	0.850685	+	0.275181i
$16$	21.4870	−	15.6112i	0.0839335	−	0.0609813i
$17$	67.7399	−	34.5152i	0.234394	−	0.119430i	−0.332849	−	0.942980i	$-0.608010\pi$
$17$	67.7399	−	34.5152i	0.234394	−	0.119430i	0.567243	+	0.823550i	$0.308010\pi$
$18$	75.0086	−	75.0086i	0.231508	−	0.231508i
$19$	21.7886	+	7.07953i	0.0603561	+	0.0196109i	0.339039	−	0.940772i	$-0.389898\pi$
$19$	21.7886	+	7.07953i	0.0603561	+	0.0196109i	−0.278683	+	0.960383i	$0.589898\pi$
$20$	−592.485	+	302.858i	−1.48121	+	0.757144i
$21$	−189.510	−	583.252i	−0.429728	−	1.32257i
$22$	−548.646	+	1076.78i	−1.13357	+	2.22475i
$23$	−495.228	+	78.4364i	−0.936159	+	0.148273i	−0.605831	−	0.795593i	$-0.707159\pi$
$23$	−495.228	+	78.4364i	−0.936159	+	0.148273i	−0.330328	+	0.943866i	$0.607159\pi$
$24$		−	557.665i		−	0.968169i
$25$	593.906	−	194.682i	0.950249	−	0.311491i
$26$	496.227			0.734064
$27$	−122.417	−	772.910i	−0.167924	−	1.06023i
$28$	1807.40	+	920.915i	2.30535	+	1.17464i
$29$	−1041.95	+	338.551i	−1.23894	+	0.402558i	−0.853947	−	0.520360i	$-0.825798\pi$
$29$	−1041.95	+	338.551i	−1.23894	+	0.402558i	−0.384998	+	0.922917i	$0.625798\pi$
$30$	−203.750	+	1297.35i	−0.226389	+	1.44150i
$31$	−48.0298	+	147.821i	−0.0499790	+	0.153820i	−0.972931	−	0.231095i	$-0.925769\pi$
$31$	−48.0298	+	147.821i	−0.0499790	+	0.153820i	0.922952	+	0.384915i	$0.125769\pi$
$32$	−661.474	−	661.474i	−0.645971	−	0.645971i
$33$	676.280	+	1327.28i	0.621011	+	1.21880i
$34$	291.722	+	401.521i	0.252355	+	0.347337i
$35$	−1542.89	−	1117.91i	−1.25950	−	0.912583i
$36$	349.898	+	254.216i	0.269983	+	0.196154i
$37$	−253.383	−	40.1319i	−0.185086	−	0.0293147i	0.0632033	−	0.998001i	$-0.479868\pi$
$37$	−253.383	−	40.1319i	−0.185086	−	0.0293147i	−0.248289	+	0.968686i	$0.579868\pi$
$38$	−23.3960	+	147.717i	−0.0162022	+	0.102297i
$39$	359.529	−	494.849i	0.236377	−	0.325345i
$40$	−1020.20	−	1400.36i	−0.637628	−	0.875223i
$41$	2493.49	−	1811.63i	1.48334	−	1.07771i	0.506878	−	0.862018i	$-0.330800\pi$
$41$	2493.49	−	1811.63i	1.48334	−	1.07771i	0.976462	−	0.215691i	$-0.0692005\pi$
$42$	3567.12	−	1817.54i	2.02218	−	1.03035i
$43$	−103.917	+	103.917i	−0.0562016	+	0.0562016i	−0.734649	−	0.678447i	$-0.762653\pi$
$43$	−103.917	+	103.917i	−0.0562016	+	0.0562016i	0.678447	+	0.734649i	$0.262653\pi$
$44$	−4686.07	−	1522.60i	−2.42049	−	0.786466i
$45$	−287.626	−	286.879i	−0.142038	−	0.141669i
$46$	−1011.47	−	3113.00i	−0.478012	−	1.47117i
$47$	−729.454	+	1431.63i	−0.330219	+	0.648091i	−0.995102	−	0.0988564i	$-0.968482\pi$
$47$	−729.454	+	1431.63i	−0.330219	+	0.648091i	0.664883	+	0.746948i	$0.268482\pi$
$48$	211.086	−	33.4327i	0.0916172	−	0.0145107i
$49$			3407.40i			1.41916i
$50$	1861.76	+	3630.53i	0.744705	+	1.45221i
$51$	611.766			0.235204
$52$	316.498	+	1998.29i	0.117048	+	0.739012i
$53$	−2026.03	−	1032.31i	−0.721263	−	0.367502i	0.0545105	−	0.998513i	$-0.482640\pi$
$53$	−2026.03	−	1032.31i	−0.721263	−	0.367502i	−0.775774	+	0.631011i	$0.782640\pi$
$54$	4858.50	−	1578.62i	1.66615	−	0.541366i
$55$	4126.36	+	2095.73i	1.36408	+	0.692802i
$56$	−1632.16	+	5023.27i	−0.520459	+	1.60181i
$57$	130.355	+	130.355i	0.0401217	+	0.0401217i
$58$	−3246.95	−	6372.49i	−0.965204	−	1.89432i
$59$	3437.49	+	4731.30i	0.987500	+	1.35918i	0.932689	+	0.360680i	$0.117455\pi$
$59$	3437.49	+	4731.30i	0.987500	+	1.35918i	0.0548106	+	0.998497i	$0.482545\pi$
$60$	−5354.34	+	6.96628i	−1.48732	+	0.00193508i
$61$	−1387.41	−	1008.01i	−0.372858	−	0.270897i	0.385537	−	0.922692i	$-0.374016\pi$
$61$	−1387.41	−	1008.01i	−0.372858	−	0.270897i	−0.758395	+	0.651795i	$0.774016\pi$
$62$	−1002.16	−	158.726i	−0.260707	−	0.0412919i
$63$	−193.731	+	1223.17i	−0.0488111	+	0.308181i
$64$	3839.28	−	5284.31i	0.937323	−	1.29011i
$65$	−2.47245	−	1900.35i	−0.000585196	−	0.449787i
$66$	−7867.28	+	5715.91i	−1.80608	+	1.31219i
$67$	−4164.25	+	2121.79i	−0.927656	+	0.472664i	−0.851455	−	0.524428i	$-0.824279\pi$
$67$	−4164.25	+	2121.79i	−0.927656	+	0.472664i	−0.0762013	+	0.997092i	$0.524279\pi$
$68$	−1430.85	+	1430.85i	−0.309439	+	0.309439i
$69$	−3837.19	−	1246.78i	−0.805963	−	0.261873i
$70$	5632.37	−	11089.8i	1.14946	−	2.26322i
$71$	2518.85	+	7752.22i	0.499672	+	1.53783i	0.809547	+	0.587056i	$0.199713\pi$
$71$	2518.85	+	7752.22i	0.499672	+	1.53783i	−0.309874	+	0.950777i	$0.600287\pi$
$72$	−511.256	+	1003.40i	−0.0986218	+	0.193556i
$73$	107.996	−	17.1049i	0.0202657	−	0.00320978i	−0.146293	−	0.989241i	$-0.546734\pi$
$73$	107.996	−	17.1049i	0.0202657	−	0.00320978i	0.166559	+	0.986031i	$0.446734\pi$
$74$		−	1674.73i		−	0.305830i
$75$	4969.34	+	773.817i	0.883439	+	0.137567i
$76$	−609.771			−0.105570
$77$	−2207.09	−	13935.0i	−0.372253	−	2.35031i
$78$	3557.81	+	1812.80i	0.584782	+	0.297961i
$79$	−3135.73	+	1018.86i	−0.502440	+	0.163253i	−0.549261	−	0.835651i	$-0.685091\pi$
$79$	−3135.73	+	1018.86i	−0.502440	+	0.163253i	0.0468216	+	0.998903i	$0.485091\pi$
$80$	468.897	−	470.118i	0.0732651	−	0.0734560i
$81$	1539.14	−	4736.97i	0.234589	−	0.721989i
$82$	14227.3	+	14227.3i	2.11590	+	2.11590i
$83$	−1746.99	−	3428.67i	−0.253592	−	0.497701i	0.728754	−	0.684775i	$-0.240100\pi$
$83$	−1746.99	−	3428.67i	−0.253592	−	0.497701i	−0.982346	+	0.187074i	$0.940100\pi$
$84$	9594.30	+	13205.4i	1.35974	+	1.87152i
$85$	1536.21	−	1119.18i	0.212624	−	0.154904i
$86$	−776.148	−	563.905i	−0.104942	−	0.0762446i
$87$	−8707.30	−	1379.10i	−1.15039	−	0.182204i
$88$	2006.98	−	12671.6i	0.259166	−	1.63631i
$89$	−1621.42	+	2231.69i	−0.204699	+	0.281744i	−0.899007	−	0.437934i	$-0.855710\pi$
$89$	−1621.42	+	2231.69i	−0.204699	+	0.281744i	0.694308	+	0.719678i	$0.255710\pi$
$90$	1555.99	−	2147.50i	0.192097	−	0.265124i
$91$	−4686.83	+	3405.18i	−0.565974	+	0.411205i
$92$	11890.8	−	6058.66i	1.40487	−	0.715815i
$93$	−884.373	+	884.373i	−0.102251	+	0.102251i
$94$	−9975.72	−	3241.31i	−1.12899	−	0.366830i
$95$	565.811	+	88.8612i	0.0626937	+	0.00984611i
$96$	−2326.12	−	7159.06i	−0.252400	−	0.776808i
$97$	1210.96	−	2376.64i	0.128702	−	0.252592i	−0.817659	−	0.575703i	$-0.804729\pi$
$97$	1210.96	−	2376.64i	0.128702	−	0.252592i	0.946361	+	0.323110i	$0.104729\pi$
$98$	−21970.0	+	3479.71i	−2.28759	+	0.362319i
$99$		−	3008.14i		−	0.306921i
$100$	−13432.6	+	9812.83i	−1.34326	+	0.981283i
$101$	3437.00			0.336928			0.168464	−	0.985708i	$-0.446119\pi$
$101$	3437.00			0.336928			0.168464	+	0.985708i	$0.446119\pi$
$102$	624.748	+	3944.50i	0.0600488	+	0.379133i
$103$	13631.0	+	6945.34i	1.28485	+	0.654665i	0.957007	−	0.290066i	$-0.0936772\pi$
$103$	13631.0	+	6945.34i	1.28485	+	0.654665i	0.327846	+	0.944731i	$0.393677\pi$
$104$	−5010.17	+	1627.90i	−0.463218	+	0.150509i
$105$	−6978.21	−	13651.6i	−0.632944	−	1.23824i
$106$	4587.05	−	14117.5i	0.408246	−	1.25645i
$107$	7093.02	+	7093.02i	0.619532	+	0.619532i	0.945411	−	0.325879i	$-0.105660\pi$
$107$	7093.02	+	7093.02i	0.619532	+	0.619532i	−0.325879	+	0.945411i	$0.605660\pi$
$108$	9455.84	+	18558.1i	0.810686	+	1.59106i
$109$	4570.57	+	6290.85i	0.384696	+	0.529488i	0.956821	−	0.290678i	$-0.0938808\pi$
$109$	4570.57	+	6290.85i	0.384696	+	0.529488i	−0.572125	+	0.820166i	$0.693881\pi$
$110$	−9298.75	+	28745.8i	−0.768492	+	2.37569i
$111$	−1670.08	−	1213.38i	−0.135547	−	0.0984808i
$112$	−1999.25	−	316.649i	−0.159379	−	0.0252431i
$113$	2474.81	−	15625.3i	0.193814	−	1.22369i	−0.678446	−	0.734650i	$-0.737346\pi$
$113$	2474.81	−	15625.3i	0.193814	−	1.22369i	0.872260	−	0.489043i	$-0.162654\pi$
$114$	−707.375	+	973.618i	−0.0544302	+	0.0749167i
$115$	−11916.5	+	3889.05i	−0.901057	+	0.294068i
$116$	23590.9	−	17139.8i	1.75319	−	1.27376i
$117$	−1100.56	+	560.763i	−0.0803974	+	0.0409645i
$118$	−26995.7	+	26995.7i	−1.93879	+	1.93879i
$119$	−5510.59	−	1790.50i	−0.389139	−	0.126439i
$120$	−2198.87	−	13767.1i	−0.152699	−	0.956052i
$121$	6065.76	+	18668.5i	0.414300	+	1.27508i
$122$	5082.52	−	9975.01i	0.341476	−	0.670184i
$123$	24495.8	−	3879.76i	1.61913	−	0.256445i
$124$		−	4136.88i		−	0.269048i
$125$	13894.2	−	7147.89i	0.889228	−	0.457465i
$126$	−8084.52			−0.509229
$127$	963.434	+	6082.88i	0.0597330	+	0.377139i	0.999387	+	0.0350127i	$0.0111472\pi$
$127$	963.434	+	6082.88i	0.0597330	+	0.377139i	−0.939654	+	0.342127i	$0.888853\pi$
$128$	24656.4	+	12563.1i	1.50491	+	0.766790i
$129$	−1124.68	+	365.430i	−0.0675848	+	0.0219596i
$130$	12250.4	−	1956.62i	0.724876	−	0.115776i
$131$	445.138	−	1369.99i	0.0259389	−	0.0798318i	−0.937249	−	0.348661i	$-0.886637\pi$
$131$	445.138	−	1369.99i	0.0259389	−	0.0798318i	0.963188	+	0.268829i	$0.0866366\pi$
$132$	−28035.6	−	28035.6i	−1.60902	−	1.60902i
$133$	−792.679	−	1555.72i	−0.0448120	−	0.0879484i
$134$	−17933.3	−	24683.1i	−0.998738	−	1.37465i
$135$	−6069.69	−	18598.2i	−0.333042	−	1.02048i
$136$	−4262.59	−	3096.95i	−0.230460	−	0.167439i
$137$	−719.545	−	113.965i	−0.0383369	−	0.00607197i	0.137237	−	0.990538i	$-0.456178\pi$
$137$	−719.545	−	113.965i	−0.0383369	−	0.00607197i	−0.175573	+	0.984466i	$0.556178\pi$
$138$	4120.28	−	26014.4i	0.216356	−	1.36602i
$139$	5084.31	−	6997.95i	0.263149	−	0.362194i	−0.656913	−	0.753967i	$-0.728138\pi$
$139$	5084.31	−	6997.95i	0.263149	−	0.362194i	0.920062	+	0.391773i	$0.128138\pi$
$140$	48250.6	+	15608.2i	2.46176	+	0.796336i
$141$	−10460.0	+	7599.61i	−0.526129	+	0.382255i
$142$	−47411.9	+	24157.6i	−2.35131	+	1.19805i
$143$	9950.32	−	9950.32i	0.486592	−	0.486592i
$144$	−410.453	−	133.364i	−0.0197942	−	0.00643153i
$145$	−24387.9	+	12466.2i	−1.15995	+	0.592925i
$146$	220.575	+	678.861i	0.0103479	+	0.0318475i
$147$	−12447.8	+	24430.1i	−0.576046	+	1.13055i
$148$	6744.06	−	1068.15i	0.307892	−	0.0487653i
$149$		−	18600.4i		−	0.837820i	−0.908028	−	0.418910i	$-0.862412\pi$
$149$		−	18600.4i		−	0.837820i	0.908028	−	0.418910i	$-0.137588\pi$
$150$	85.4304	+	32831.2i	0.00379691	+	1.45917i
$151$	−11526.1			−0.505508			−0.252754	−	0.967531i	$-0.581336\pi$
$151$	−11526.1			−0.505508			−0.252754	+	0.967531i	$0.581336\pi$
$152$	−248.374	−	1568.17i	−0.0107503	−	0.0678746i
$153$	−1100.74	−	560.854i	−0.0470220	−	0.0239589i
$154$	87595.1	−	28461.4i	3.69350	−	1.20009i
$155$	−602.863	+	3838.64i	−0.0250931	+	0.159777i
$156$	−5030.86	+	15483.4i	−0.206725	+	0.636234i
$157$	−18123.4	−	18123.4i	−0.735257	−	0.735257i	0.236399	−	0.971656i	$-0.424033\pi$
$157$	−18123.4	−	18123.4i	−0.735257	−	0.735257i	−0.971656	+	0.236399i	$0.924033\pi$
$158$	−9771.59	−	19177.8i	−0.391427	−	0.768220i
$159$	−10754.9	−	14802.8i	−0.425413	−	0.585531i
$160$	−18938.1	−	13721.7i	−0.739768	−	0.536004i
$161$	30915.2	+	22461.2i	1.19267	+	0.866524i
$162$	32114.5	+	5086.44i	1.22369	+	0.193813i
$163$	−3115.28	+	19669.1i	−0.117252	+	0.740302i	0.857079	+	0.515185i	$0.172277\pi$
$163$	−3115.28	+	19669.1i	−0.117252	+	0.740302i	−0.974332	+	0.225118i	$0.927723\pi$
$164$	−48218.5	+	66367.1i	−1.79278	+	2.46754i
$165$	21928.8	+	30100.0i	0.805467	+	1.10560i
$166$	20323.0	−	14765.6i	0.737518	−	0.535838i
$167$	20621.3	−	10507.1i	0.739407	−	0.376747i	−0.0433615	−	0.999059i	$-0.513807\pi$
$167$	20621.3	−	10507.1i	0.739407	−	0.376747i	0.782769	+	0.622313i	$0.213807\pi$
$168$	−30052.9	+	30052.9i	−1.06480	+	1.06480i
$169$	21667.8	+	7040.29i	0.758650	+	0.246500i
$170$	8784.96	+	8762.14i	0.303978	+	0.303188i
$171$	−115.039	−	354.053i	−0.00393416	−	0.0121081i
$172$	1775.79	−	3485.18i	0.0600253	−	0.117806i
$173$	−43658.6	+	6914.84i	−1.45874	+	0.231042i	−0.834853	−	0.550473i	$-0.814447\pi$
$173$	−43658.6	+	6914.84i	−1.45874	+	0.231042i	−0.623886	+	0.781515i	$0.714447\pi$
$174$		−	57550.6i		−	1.90087i
$175$	−42497.5	−	21514.4i	−1.38767	−	0.702512i
$176$	4916.73			0.158727
$177$	7361.67	+	46479.8i	0.234980	+	1.48360i
$178$	−16045.2	−	8175.42i	−0.506412	−	0.258030i
$179$	−34704.4	+	11276.1i	−1.08312	+	0.351928i	−0.795586	−	0.605841i	$-0.792837\pi$
$179$	−34704.4	+	11276.1i	−1.08312	+	0.351928i	−0.287538	+	0.957769i	$0.592837\pi$
$180$	9640.33	+	4896.21i	0.297541	+	0.151117i
$181$	3827.28	−	11779.1i	0.116824	−	0.359548i	−0.875499	−	0.483220i	$-0.839467\pi$
$181$	3827.28	−	11779.1i	0.116824	−	0.359548i	0.992323	+	0.123672i	$0.0394671\pi$
$182$	−26742.0	−	26742.0i	−0.807330	−	0.807330i
$183$	−6264.90	−	12295.6i	−0.187073	−	0.367152i
$184$	20424.7	+	28112.2i	0.603282	+	0.830347i
$185$	−6413.52	+	8.34433i	−0.187393	+	0.000243808i
$186$	−6605.33	−	4799.06i	−0.190928	−	0.138717i
$187$	13900.9	+	2201.68i	0.397520	+	0.0629610i
$188$	6690.03	−	42239.2i	0.189283	−	1.19509i
$189$	−35055.5	+	48249.7i	−0.981369	+	1.35074i
$190$	4.86456	+	3738.94i	0.000134752	+	0.103572i
$191$	−5672.25	+	4121.13i	−0.155485	+	0.112966i	−0.662808	−	0.748790i	$-0.730635\pi$
$191$	−5672.25	+	4121.13i	−0.155485	+	0.112966i	0.507323	+	0.861756i	$0.330635\pi$
$192$	46831.0	−	23861.6i	1.27037	−	0.647287i
$193$	39502.8	−	39502.8i	1.06051	−	1.06051i	0.0624597	−	0.998047i	$-0.480106\pi$
$193$	39502.8	−	39502.8i	1.06051	−	1.06051i	0.998047	−	0.0624597i	$-0.0198945\pi$
$194$	16560.6	+	5380.87i	0.440020	+	0.142971i
$195$	6924.55	−	13634.0i	0.182105	−	0.358554i
$196$	−28025.3	−	86253.0i	−0.729521	−	2.24524i
$197$	19878.1	−	39013.0i	0.512204	−	1.00526i	−0.479600	−	0.877487i	$-0.659218\pi$
$197$	19878.1	−	39013.0i	0.512204	−	1.00526i	0.991804	−	0.127769i	$-0.0407816\pi$
$198$	19395.7	−	3071.97i	0.494737	−	0.0783586i
$199$		−	5075.53i		−	0.128167i	−0.997945	−	0.0640834i	$-0.979588\pi$
$199$		−	5075.53i		−	0.128167i	0.997945	−	0.0640834i	$-0.0204124\pi$
$200$	−30707.5	−	30548.1i	−0.767687	−	0.763702i
$201$	−37607.8			−0.930862
$202$	3509.94	+	22160.9i	0.0860194	+	0.543105i
$203$	74396.2	+	37906.8i	1.80534	+	0.919866i
$204$	−15485.9	+	5031.67i	−0.372114	+	0.120907i
$205$	54413.9	−	54555.7i	1.29480	−	1.29817i
$206$	−30861.4	+	94981.7i	−0.727247	+	2.23824i
$207$	5761.16	+	5761.16i	0.134453	+	0.134453i
$208$	−916.554	−	1798.84i	−0.0211851	−	0.0415782i
$209$	2492.87	+	3431.14i	0.0570699	+	0.0785499i
$210$	80895.3	−	58934.9i	1.83436	−	1.33639i
$211$	28085.0	+	20404.9i	0.630826	+	0.458322i	0.856686	−	0.515838i	$-0.172519\pi$
$211$	28085.0	+	20404.9i	0.630826	+	0.458322i	−0.225860	+	0.974160i	$0.572519\pi$
$212$	59776.3	+	9467.64i	1.33002	+	0.210654i
$213$	−10260.6	+	64783.0i	−0.226159	+	1.42791i
$214$	−38490.4	+	52977.4i	−0.840474	+	1.15681i
$215$	−2155.66	+	2975.14i	−0.0466341	+	0.0643622i
$216$	−43875.2	+	31877.2i	−0.940397	+	0.683238i
$217$	10554.5	−	5377.79i	0.224139	−	0.114205i
$218$	−35894.2	+	35894.2i	−0.755285	+	0.755285i
$219$	836.789	+	271.889i	0.0174473	+	0.00566896i
$220$	−121689.	−	19111.4i	−2.51424	−	0.394864i
$221$	−1785.83	−	5496.22i	−0.0365641	−	0.112533i
$222$	6118.04	−	12007.3i	0.124139	−	0.243636i
$223$	−55426.7	+	8778.72i	−1.11457	+	0.176531i	−0.686442	−	0.727185i	$-0.740828\pi$
$223$	−55426.7	+	8778.72i	−1.11457	+	0.176531i	−0.428133	+	0.903716i	$0.640828\pi$
$224$			71294.5i			1.42089i
$225$	−8231.82	−	5948.10i	−0.162604	−	0.117493i
$226$	103275.			2.02199
$227$	−4694.93	−	29642.6i	−0.0911124	−	0.575261i	−0.990436	−	0.137976i	$-0.955940\pi$
$227$	−4694.93	−	29642.6i	−0.0911124	−	0.575261i	0.899323	−	0.437285i	$-0.144060\pi$
$228$	−4371.89	−	2227.59i	−0.0841007	−	0.0428514i
$229$	11217.9	−	3644.91i	0.213914	−	0.0695049i	−0.200100	−	0.979776i	$-0.564127\pi$
$229$	11217.9	−	3644.91i	0.213914	−	0.0695049i	0.414014	+	0.910271i	$0.364127\pi$
$230$	−37244.9	−	72862.6i	−0.704062	−	1.37737i
$231$	35082.5	−	107973.i	0.657456	−	2.02344i
$232$	53688.2	+	53688.2i	0.997477	+	0.997477i
$233$	−5834.95	−	11451.7i	−0.107479	−	0.210940i	0.831002	−	0.556269i	$-0.187768\pi$
$233$	−5834.95	−	11451.7i	−0.107479	−	0.210940i	−0.938482	+	0.345328i	$0.887768\pi$
$234$	−4739.56	−	6523.45i	−0.0865579	−	0.119137i
$235$	−12363.2	+	38219.1i	−0.223869	+	0.692062i
$236$	−125929.	−	91492.5i	−2.26100	−	1.64271i
$237$	−26204.3	−	4150.36i	−0.466527	−	0.0738906i
$238$	5917.13	−	37359.3i	0.104462	−	0.659546i
$239$	62490.8	−	86011.2i	1.09401	−	1.50577i	0.250910	−	0.968011i	$-0.419270\pi$
$239$	62490.8	−	86011.2i	1.09401	−	1.50577i	0.843097	−	0.537761i	$-0.180730\pi$
$240$	5079.28	−	1657.67i	0.0881819	−	0.0287789i
$241$	−26513.5	+	19263.2i	−0.456492	+	0.331661i	−0.792153	−	0.610322i	$-0.791040\pi$
$241$	−26513.5	+	19263.2i	−0.456492	+	0.331661i	0.335662	+	0.941983i	$0.391040\pi$
$242$	−114175.	+	58175.0i	−1.94957	+	0.993358i
$243$	−16480.6	+	16480.6i	−0.279101	+	0.279101i
$244$	43410.7	+	14105.0i	0.729150	+	0.236915i
$245$	13435.3	+	84118.9i	0.223829	+	1.40140i
$246$	50031.3	+	153980.i	0.826744	+	2.54446i
$247$	790.611	−	1551.66i	0.0129589	−	0.0254333i
$248$	10639.0	−	1685.05i	0.172981	−	0.0273974i
$249$		−	30964.6i		−	0.499421i
$250$	60276.7	+	82286.4i	0.964427	+	1.31658i
$251$	−50401.9			−0.800017			−0.400009	−	0.916511i	$-0.630993\pi$
$251$	−50401.9			−0.800017			−0.400009	+	0.916511i	$0.630993\pi$
$252$	−5156.37	−	32556.1i	−0.0811976	−	0.512662i
$253$	−82703.7	−	42139.6i	−1.29206	−	0.658339i
$254$	−38236.9	+	12423.9i	−0.592673	+	0.192571i
$255$	15102.7	−	2412.18i	0.232260	−	0.0370963i
$256$	−23528.9	+	72414.5i	−0.359022	+	1.10496i
$257$	42828.0	+	42828.0i	0.648428	+	0.648428i	0.952613	−	0.304185i	$-0.0983841\pi$
$257$	42828.0	+	42828.0i	0.648428	+	0.648428i	−0.304185	+	0.952613i	$0.598384\pi$
$258$	−3504.74	−	6878.44i	−0.0526522	−	0.103336i
$259$	11492.2	+	15817.7i	0.171319	+	0.235800i
$260$	15692.6	+	48084.0i	0.232139	+	0.711302i
$261$	14402.5	+	10464.0i	0.211426	+	0.153610i
$262$	9287.93	+	1471.06i	0.135306	+	0.0214303i
$263$	10827.9	−	68364.7i	0.156543	−	0.988372i	−0.776895	−	0.629631i	$-0.783206\pi$
$263$	10827.9	−	68364.7i	0.156543	−	0.988372i	0.933437	−	0.358741i	$-0.116794\pi$
$264$	60680.7	−	83519.9i	0.870649	−	1.19835i
$265$	−54087.2	−	17496.2i	−0.770198	−	0.249145i
$266$	9221.36	−	6699.71i	0.130326	−	0.0946875i
$267$	−19777.8	+	10077.3i	−0.277432	+	0.141359i
$268$	87960.0	−	87960.0i	1.22466	−	1.22466i
$269$	101397.	+	32945.8i	1.40126	+	0.455298i	0.909599	−	0.415486i	$-0.136389\pi$
$269$	101397.	+	32945.8i	1.40126	+	0.455298i	0.491665	+	0.870785i	$0.336389\pi$
$270$	113718.	−	58128.6i	1.55991	−	0.797374i
$271$	−24412.7	−	75134.5i	−0.332412	−	1.02306i	−0.967983	−	0.251017i	$-0.919235\pi$
$271$	−24412.7	−	75134.5i	−0.332412	−	1.02306i	0.635570	−	0.772043i	$-0.280765\pi$
$272$	916.702	−	1799.13i	0.0123905	−	0.0243178i
$273$	−46043.0	+	7292.49i	−0.617786	+	0.0978477i
$274$		−	4755.81i		−	0.0633467i
$275$	110131.	+	35467.2i	1.45628	+	0.468988i
$276$	107387.			1.40972
$277$	2909.60	+	18370.5i	0.0379205	+	0.239420i	0.999367	−	0.0355710i	$-0.0113250\pi$
$277$	2909.60	+	18370.5i	0.0379205	+	0.239420i	−0.961447	+	0.274991i	$0.911325\pi$
$278$	50313.1	+	25635.8i	0.651016	+	0.331709i
$279$	2402.01	−	780.459i	0.0308579	−	0.0100263i
$280$	−20486.6	+	130446.i	−0.261309	+	1.66385i
$281$	6949.02	−	21386.9i	0.0880058	−	0.270854i	−0.897362	−	0.441295i	$-0.854519\pi$
$281$	6949.02	−	21386.9i	0.0880058	−	0.270854i	0.985368	+	0.170441i	$0.0545192\pi$
$282$	−59682.2	−	59682.2i	−0.750493	−	0.750493i
$283$	−51433.7	−	100944.i	−0.642207	−	1.26040i	−0.950976	−	0.309264i	$-0.899917\pi$
$283$	−51433.7	−	100944.i	−0.642207	−	1.26040i	0.308770	−	0.951137i	$-0.400083\pi$
$284$	−127521.	−	175518.i	−1.58105	−	2.17613i
$285$	3732.08	+	2704.11i	0.0459475	+	0.0332916i
$286$	74318.4	+	53995.5i	0.908583	+	0.660124i
$287$	−232006.	−	36746.1i	−2.81666	−	0.446116i
$288$	−2377.93	+	15013.7i	−0.0286691	+	0.181010i
$289$	−45695.0	+	62893.8i	−0.547108	+	0.753030i
$290$	−105284.	−	144516.i	−1.25189	−	1.71838i
$291$	17364.5	−	12616.0i	0.205058	−	0.148983i
$292$	−2593.06	+	1321.23i	−0.0304122	+	0.0154958i
$293$	−54321.7	+	54321.7i	−0.632759	+	0.632759i	−0.948759	−	0.316000i	$-0.897660\pi$
$293$	−54321.7	+	54321.7i	−0.632759	+	0.632759i	0.316000	+	0.948759i	$0.397660\pi$
$294$	−170231.	−	55311.4i	−1.96944	−	0.639911i
$295$	103517.	+	103248.i	1.18951	+	1.18642i
$296$	5494.04	+	16908.9i	0.0627059	+	0.192989i
$297$	65767.9	−	129077.i	0.745592	−	1.46331i
$298$	119931.	−	18995.1i	1.35051	−	0.213900i
$299$			38113.5i			0.426321i
$300$	−132156.	+	21284.0i	−1.46840	+	0.236489i
$301$	11200.3			0.123622
$302$	−11770.7	−	74317.2i	−0.129059	−	0.814845i
$303$	24642.4	+	12555.9i	0.268409	+	0.136761i
$304$	578.690	−	188.028i	0.00626180	−	0.00203458i
$305$	−38225.6	−	19414.3i	−0.410917	−	0.208700i
$306$	2492.14	−	7670.02i	0.0266152	−	0.0819131i
$307$	31876.9	+	31876.9i	0.338220	+	0.338220i	0.855697	−	0.517477i	$-0.173129\pi$
$307$	31876.9	+	31876.9i	0.338220	+	0.338220i	−0.517477	+	0.855697i	$0.673129\pi$
$308$	170482.	+	334589.i	1.79712	+	3.52704i
$309$	72358.1	+	99592.4i	0.757827	+	1.04306i
$310$	−25366.2	+	33.0027i	−0.263956	+	0.000343421i
$311$	13676.3	+	9936.43i	0.141400	+	0.102733i	0.656236	−	0.754555i	$-0.272147\pi$
$311$	13676.3	+	9936.43i	0.141400	+	0.102733i	−0.514837	+	0.857288i	$0.672147\pi$
$312$	−41868.5	−	6631.32i	−0.430109	−	0.0681225i
$313$	−27000.8	+	170476.i	−0.275605	+	1.74010i	0.329679	+	0.944093i	$0.393060\pi$
$313$	−27000.8	+	170476.i	−0.275605	+	1.74010i	−0.605284	+	0.796010i	$0.706940\pi$
$314$	98346.6	−	135362.i	0.997470	−	1.37290i
$315$	40.2812	+	30960.4i	0.000405958	+	0.312023i
$316$	70996.0	−	51581.6i	0.710984	−	0.516560i
$317$	77665.5	−	39572.5i	0.772875	−	0.393800i	−0.0226319	−	0.999744i	$-0.507205\pi$
$317$	77665.5	−	39572.5i	0.772875	−	0.393800i	0.795507	+	0.605944i	$0.207205\pi$
$318$	84461.4	−	84461.4i	0.835226	−	0.835226i
$319$	−192889.	−	62673.3i	−1.89551	−	0.615887i
$320$	73944.6	−	145592.i	0.722116	−	1.42180i
$321$	24943.1	+	76767.0i	0.242070	+	0.745014i
$322$	−113252.	+	222270.i	−1.09228	+	2.14373i
$323$	1720.31	−	272.470i	0.0164893	−	0.00261164i
$324$			132568.i			1.26284i
$325$	−7554.08	−	46904.3i	−0.0715179	−	0.444065i
$326$	−130002.			−1.22325
$327$	9788.27	+	61800.7i	0.0915399	+	0.577960i
$328$	−190320.	−	96972.7i	−1.76903	−	0.901367i
$329$	116462.	−	37840.9i	1.07595	−	0.349599i
$330$	−171683.	+	172130.i	−1.57652	+	1.58062i
$331$	58044.2	−	178642.i	0.529789	−	1.63052i	−0.224859	−	0.974391i	$-0.572192\pi$
$331$	58044.2	−	178642.i	0.529789	−	1.63052i	0.754648	−	0.656130i	$-0.227808\pi$
$332$	72422.5	+	72422.5i	0.657049	+	0.657049i
$333$	1892.53	+	3714.30i	0.0170669	+	0.0334957i
$334$	88805.8	+	122231.i	0.796065	+	1.09569i
$335$	−94437.0	+	68800.4i	−0.841497	+	0.613058i
$336$	−13177.3	−	9573.85i	−0.116720	−	0.0848024i
$337$	155014.	+	24551.8i	1.36493	+	0.216184i	0.795548	−	0.605890i	$-0.207183\pi$
$337$	155014.	+	24551.8i	1.36493	+	0.216184i	0.569381	+	0.822074i	$0.307183\pi$
$338$	−23266.3	+	146898.i	−0.203655	+	1.28582i
$339$	74825.5	−	102988.i	0.651104	−	0.896168i
$340$	−29681.7	+	40965.3i	−0.256762	+	0.354371i
$341$	−23277.9	+	16912.4i	−0.200187	+	0.145444i
$342$	2165.36	−	1103.30i	0.0185130	−	0.00943285i
$343$	54235.6	−	54235.6i	0.460995	−	0.460995i
$344$	9686.32	+	3147.28i	0.0818544	+	0.0265961i
$345$	−99645.2	−	15649.4i	−0.837178	−	0.131480i
$346$	−89170.1	−	274437.i	−0.744847	−	2.29240i
$347$	−57346.1	+	112548.i	−0.476261	+	0.934714i	0.520467	+	0.853882i	$0.325758\pi$
$347$	−57346.1	+	112548.i	−0.476261	+	0.934714i	−0.996728	+	0.0808322i	$0.974242\pi$
$348$	231754.	−	36706.3i	1.91368	−	0.303097i
$349$			3150.58i			0.0258666i	0.999916	+	0.0129333i	$0.00411692\pi$
$349$			3150.58i			0.0258666i	−0.999916	+	0.0129333i	$0.995883\pi$
$350$	95320.0	−	295983.i	0.778123	−	2.41619i
$351$	−59484.3			−0.482823
$352$	−27090.6	−	171043.i	−0.218642	−	1.38045i
$353$	34573.0	+	17615.8i	0.277452	+	0.141369i	0.587180	−	0.809456i	$-0.300238\pi$
$353$	34573.0	+	17615.8i	0.277452	+	0.141369i	−0.309728	+	0.950825i	$0.600238\pi$
$354$	−292171.	+	94932.2i	−2.33148	+	0.757542i
$355$	92749.9	+	181448.i	0.735964	+	1.43978i
$356$	22688.4	−	69827.6i	0.179021	−	0.550969i
$357$	−32968.5	−	32968.5i	−0.258680	−	0.258680i
$358$	−108146.	−	212249.i	−0.843811	−	1.65607i
$359$	−6162.14	−	8481.45i	−0.0478126	−	0.0658084i	0.784441	−	0.620203i	$-0.212950\pi$
$359$	−6162.14	−	8481.45i	−0.0478126	−	0.0658084i	−0.832254	+	0.554395i	$0.812950\pi$
$360$	−8665.04	+	26786.8i	−0.0668599	+	0.206688i
$361$	−105007.	−	76292.3i	−0.805759	−	0.585418i
$362$	79857.3	+	12648.1i	0.609393	+	0.0965183i
$363$	−24709.1	+	156007.i	−0.187518	+	1.18394i
$364$	90632.8	−	124745.i	0.684041	−	0.941502i
$365$	2598.66	−	848.097i	0.0195058	−	0.00636590i
$366$	72880.6	−	52950.8i	0.544064	−	0.395285i
$367$	159860.	−	81452.8i	1.18688	−	0.604747i	0.254801	−	0.966994i	$-0.417990\pi$
$367$	159860.	−	81452.8i	1.18688	−	0.604747i	0.932082	+	0.362246i	$0.117990\pi$
$368$	−9416.47	+	9416.47i	−0.0695333	+	0.0695333i
$369$	−47631.7	−	15476.5i	−0.349819	−	0.113663i
$370$	−6603.42	−	41344.2i	−0.0482354	−	0.302003i
$371$	53552.0	+	164816.i	0.389070	+	1.19743i
$372$	15112.7	−	29660.3i	0.109208	−	0.214333i
$373$	−5719.76	+	905.922i	−0.0411112	+	0.00651138i	−0.176956	−	0.984219i	$-0.556625\pi$
$373$	−5719.76	+	905.922i	−0.0411112	+	0.00651138i	0.135845	+	0.990730i	$0.456625\pi$
$374$			91877.5i			0.656850i
$375$	125730.	−	490.746i	0.894079	−	0.00348975i
$376$	111353.			0.787640
$377$	13027.7	+	82253.7i	0.0916611	+	0.578725i
$378$	−346901.	−	176755.i	−2.42785	−	1.23705i
$379$	−150308.	+	48838.2i	−1.04642	+	0.340002i	−0.781261	−	0.624204i	$-0.785423\pi$
$379$	−150308.	+	48838.2i	−1.04642	+	0.340002i	−0.265156	+	0.964206i	$0.585423\pi$
$380$	−15053.5	+	2404.32i	−0.104248	+	0.0166504i
$381$	−15314.2	+	47132.2i	−0.105498	+	0.324689i
$382$	−32364.5	−	32364.5i	−0.221790	−	0.221790i
$383$	28323.9	+	55588.7i	0.193088	+	0.378956i	0.967171	−	0.254128i	$-0.0817886\pi$
$383$	28323.9	+	55588.7i	0.193088	+	0.378956i	−0.774083	+	0.633084i	$0.781789\pi$
$384$	130885.	+	180148.i	0.887621	+	1.22171i
$385$	−109432.	−	335312.i	−0.738283	−	2.26218i
$386$	295045.	+	214362.i	1.98022	+	1.43871i
$387$	2358.63	+	373.570i	0.0157484	+	0.00249431i
$388$	−11106.1	+	70120.9i	−0.0737728	+	0.465783i
$389$	78066.6	−	107449.i	0.515901	−	0.710076i	−0.469000	−	0.883198i	$-0.655385\pi$
$389$	78066.6	−	107449.i	0.515901	−	0.710076i	0.984900	+	0.173122i	$0.0553855\pi$
$390$	94979.9	+	30724.3i	0.624457	+	0.202001i
$391$	−30839.5	+	22406.2i	−0.201722	+	0.146560i
$392$	210405.	−	107207.i	1.36925	−	0.697670i
$393$	8196.32	−	8196.32i	0.0530681	−	0.0530681i
$394$	271845.	+	88327.8i	1.75117	+	0.568991i
$395$	−73394.6	+	37516.8i	−0.470403	+	0.240454i
$396$	24741.4	+	76146.2i	0.157774	+	0.485577i
$397$	−63451.9	+	124531.i	−0.402591	+	0.790128i	−0.999930	−	0.0118603i	$-0.996225\pi$
$397$	−63451.9	+	124531.i	−0.402591	+	0.790128i	0.597339	+	0.801989i	$0.296225\pi$
$398$	32725.7	−	5183.23i	0.206596	−	0.0327216i
$399$		−	14049.9i		−	0.0882524i
$400$	9722.03	−	13454.7i	0.0607627	−	0.0840919i
$401$	−303762.			−1.88906			−0.944529	−	0.328429i	$-0.893481\pi$
$401$	−303762.			−1.88906			−0.944529	+	0.328429i	$0.893481\pi$
$402$	−38405.8	−	242485.i	−0.237654	−	1.50049i
$403$	10527.0	+	5363.76i	0.0648176	+	0.0330262i
$404$	−87002.3	+	28268.8i	−0.533050	+	0.173198i
$405$	19319.0	−	123011.i	0.117781	−	0.749952i
$406$	−168438.	+	518398.i	−1.02185	+	3.14493i
$407$	−33581.5	−	33581.5i	−0.202727	−	0.202727i
$408$	−19247.9	−	37776.2i	−0.115628	−	0.226933i
$409$	−158835.	−	218617.i	−0.949508	−	1.30689i	−0.951746	−	0.306888i	$-0.900712\pi$
$409$	−158835.	−	218617.i	−0.949508	−	1.30689i	0.00223805	−	0.999997i	$-0.499288\pi$
$410$	407329.	+	295133.i	2.42313	+	1.75570i
$411$	−4742.61	−	3445.71i	−0.0280759	−	0.0203983i
$412$	−402172.	−	63697.7i	−2.36928	−	0.375258i
$413$	69724.1	−	440221.i	0.408774	−	2.58090i
$414$	−31263.0	+	43029.8i	−0.182402	+	0.251055i
$415$	−56647.3	−	77755.4i	−0.328915	−	0.451476i
$416$	−57528.0	+	41796.5i	−0.332424	+	0.241520i
$417$	62017.7	−	31599.6i	0.356651	−	0.181723i
$418$	−19577.3	+	19577.3i	−0.112047	+	0.112047i
$419$	38645.4	+	12556.7i	0.220125	+	0.0715231i	0.417003	−	0.908905i	$-0.363080\pi$
$419$	38645.4	+	12556.7i	0.220125	+	0.0715231i	−0.196878	+	0.980428i	$0.563080\pi$
$420$	288924.	+	288173.i	1.63789	+	1.63364i
$421$	94008.8	+	289329.i	0.530401	+	1.63241i	0.753382	+	0.657583i	$0.228421\pi$
$421$	94008.8	+	289329.i	0.530401	+	1.63241i	−0.222981	+	0.974823i	$0.571579\pi$
$422$	−102885.	+	201922.i	−0.577731	+	1.13386i
$423$	25787.6	−	4084.35i	0.144122	−	0.0228266i
$424$			157586.i			0.876567i
$425$	33511.7	−	33686.5i	0.185532	−	0.186500i
$426$	−428182.			−2.35944
$427$	20445.9	+	129090.i	0.112137	+	0.708008i
$428$	−237888.	−	121210.i	−1.29863	−	0.661683i
$429$	107691.	−	34991.0i	0.585148	−	0.190126i
$430$	−21384.3	−	10860.8i	−0.115653	−	0.0587390i
$431$	36647.5	−	112789.i	0.197283	−	0.607175i	−0.802659	−	0.596438i	$-0.796582\pi$
$431$	36647.5	−	112789.i	0.197283	−	0.607175i	0.999942	−	0.0107373i	$-0.00341785\pi$
$432$	−14696.4	−	14696.4i	−0.0787488	−	0.0787488i
$433$	−4627.73	−	9082.44i	−0.0246827	−	0.0484425i	0.878336	−	0.478044i	$-0.158654\pi$
$433$	−4627.73	−	9082.44i	−0.0246827	−	0.0484425i	−0.903019	+	0.429601i	$0.858654\pi$
$434$	45453.0	+	62560.7i	0.241314	+	0.332141i
$435$	−220396.	+	286.746i	−1.16473	+	0.00151537i
$436$	−167438.	−	121651.i	−0.880808	−	0.639944i
$437$	−11345.6	−	1796.97i	−0.0594107	−	0.00940973i
$438$	−898.522	+	5673.05i	−0.00468361	+	0.0295711i
$439$	−29519.8	+	40630.5i	−0.153174	+	0.210826i	−0.878707	−	0.477362i	$-0.841593\pi$
$439$	−29519.8	+	40630.5i	−0.153174	+	0.210826i	0.725533	+	0.688187i	$0.241593\pi$
$440$	−417.297	−	320738.i	−0.00215546	−	1.65670i
$441$	44794.0	−	32544.8i	0.230326	−	0.167342i
$442$	33614.4	−	17127.4i	0.172060	−	0.0876691i
$443$	176391.	−	176391.i	0.898812	−	0.898812i	−0.0965189	−	0.995331i	$-0.530771\pi$
$443$	176391.	−	176391.i	0.898812	−	0.898812i	0.995331	+	0.0965189i	$0.0307708\pi$
$444$	52255.2	+	16978.7i	0.265072	+	0.0861271i
$445$	−31228.6	+	61487.2i	−0.157700	+	0.310502i
$446$	−113206.	−	348411.i	−0.569113	−	1.75155i
$447$	67950.3	−	133360.i	0.340077	−	0.667438i
$448$	−491676.	+	77873.8i	−2.44976	+	0.388003i
$449$			46215.1i			0.229241i	0.993409	+	0.114620i	$0.0365651\pi$
$449$			46215.1i			0.229241i	−0.993409	+	0.114620i	$0.963435\pi$
$450$	29945.2	−	59150.8i	0.147878	−	0.292103i
$451$	570570.			2.80515
$452$	65869.8	+	415886.i	0.322411	+	2.03562i
$453$	−82639.0	−	42106.7i	−0.402706	−	0.205189i
$454$	186333.	−	60543.3i	0.904021	−	0.293734i
$455$	−102278.	+	102544.i	−0.494036	+	0.495323i
$456$	3948.01	−	12150.7i	0.0189867	−	0.0584349i
$457$	100912.	+	100912.i	0.483182	+	0.483182i	0.906146	−	0.422964i	$-0.139010\pi$
$457$	100912.	+	100912.i	0.483182	+	0.483182i	−0.422964	+	0.906146i	$0.639010\pi$
$458$	34957.3	+	68607.6i	0.166651	+	0.327070i
$459$	−34969.7	−	48131.6i	−0.165984	−	0.228457i
$460$	269660.	−	196456.i	1.27439	−	0.928431i
$461$	−99771.4	−	72488.1i	−0.469466	−	0.341087i	0.327767	−	0.944759i	$-0.393704\pi$
$461$	−99771.4	−	72488.1i	−0.469466	−	0.341087i	−0.797233	+	0.603672i	$0.793704\pi$
$462$	732007.	+	115939.i	3.42950	+	0.543180i
$463$	−25789.9	+	162831.i	−0.120306	+	0.759584i	0.851596	+	0.524199i	$0.175635\pi$
$463$	−25789.9	+	162831.i	−0.120306	+	0.759584i	−0.971902	+	0.235385i	$0.924365\pi$
$464$	−17103.2	+	23540.6i	−0.0794405	+	0.109341i
$465$	−18345.5	+	25319.7i	−0.0848446	+	0.117099i
$466$	67878.9	−	49316.9i	0.312581	−	0.227104i
$467$	−312220.	+	159084.i	−1.43162	+	0.729445i	−0.986150	−	0.165854i	$-0.946962\pi$
$467$	−312220.	+	159084.i	−1.43162	+	0.729445i	−0.445466	+	0.895299i	$0.646962\pi$
$468$	23246.8	−	23246.8i	0.106138	−	0.106138i
$469$	338759.	+	110069.i	1.54008	+	0.500404i
$470$	−259052.	−	40684.4i	−1.17271	−	0.184176i
$471$	−63732.0	−	196147.i	−0.287287	−	0.884178i
$472$	184001.	−	361123.i	0.825919	−	1.62096i
$473$	−26870.7	+	4255.90i	−0.120104	+	0.0190226i
$474$		−	173197.i		−	0.770874i
$475$	14318.6	−	37.2586i	0.0634620	−	0.000165135i
$476$	154219.			0.680648
$477$	5780.11	+	36494.2i	0.0254038	+	0.160394i
$478$	618394.	+	315087.i	2.70651	+	1.37903i
$479$	−47521.6	+	15440.7i	−0.207119	+	0.0672971i	−0.410739	−	0.911753i	$-0.634729\pi$
$479$	−47521.6	+	15440.7i	−0.207119	+	0.0672971i	0.203620	+	0.979050i	$0.434729\pi$
$480$	−85653.2	−	167565.i	−0.371759	−	0.727277i
$481$	−6026.06	+	18546.3i	−0.0260461	+	0.0801617i
$482$	−151280.	−	151280.i	−0.651159	−	0.651159i
$483$	139599.	+	273978.i	0.598395	+	1.17442i
$484$	−307090.	−	422674.i	−1.31092	−	1.80432i
$485$	20524.0	−	63447.2i	0.0872527	−	0.269730i
$486$	−123093.	−	89432.4i	−0.521148	−	0.378636i
$487$	17151.7	+	2716.56i	0.0723184	+	0.0114541i	0.192489	−	0.981299i	$-0.438344\pi$
$487$	17151.7	+	2716.56i	0.0723184	+	0.0114541i	−0.120170	+	0.992753i	$0.538344\pi$
$488$	−18592.2	+	117386.i	−0.0780711	+	0.492922i
$489$	−94190.0	+	129641.i	−0.393901	+	0.542158i
$490$	−528655.	+	172531.i	−2.20181	+	0.718581i
$491$	−269434.	+	195755.i	−1.11761	+	0.811990i	−0.983845	−	0.179023i	$-0.942706\pi$
$491$	−269434.	+	195755.i	−1.11761	+	0.811990i	−0.133763	+	0.991013i	$0.542706\pi$
$492$	−588163.	+	299684.i	−2.42978	+	1.23804i
$493$	−58896.6	+	58896.6i	−0.242324	+	0.242324i
$494$	10812.1	+	3513.06i	0.0443052	+	0.0143956i
$495$	−11861.0	−	74262.2i	−0.0484075	−	0.303080i
$496$	1275.64	+	3926.02i	0.00518520	+	0.0159584i
$497$	282030.	−	553514.i	1.14178	−	2.24087i
$498$	199652.	−	31621.7i	0.805034	−	0.127505i
$499$			179168.i			0.719549i	0.933039	+	0.359775i	$0.117146\pi$
$499$			179168.i			0.719549i	−0.933039	+	0.359775i	$0.882854\pi$
$500$	−292919.	+	295215.i	−1.17168	+	1.18086i
$501$	186233.			0.741963
$502$	−51471.4	−	324978.i	−0.204248	−	1.28957i
$503$	43436.2	+	22131.8i	0.171678	+	0.0874745i	0.537718	−	0.843125i	$-0.319287\pi$
$503$	43436.2	+	22131.8i	0.171678	+	0.0874745i	−0.366040	+	0.930599i	$0.619287\pi$
$504$	81625.5	−	26521.7i	0.321340	−	0.104410i
$505$	84849.6	−	13552.0i	0.332711	−	0.0531401i
$506$	187246.	−	576285.i	0.731328	−	2.25080i
$507$	129633.	+	129633.i	0.504312	+	0.504312i
$508$	−74418.4	−	146054.i	−0.288372	−	0.565962i
$509$	−118530.	−	163143.i	−0.457502	−	0.629697i	0.516486	−	0.856295i	$-0.327240\pi$
$509$	−118530.	−	163143.i	−0.457502	−	0.629697i	−0.973988	+	0.226598i	$0.927240\pi$
$510$	30976.3	+	94915.0i	0.119094	+	0.364917i
$511$	−6741.77	−	4898.18i	−0.0258186	−	0.0187583i
$512$	−53627.2	−	8493.72i	−0.204572	−	0.0324010i
$513$	2804.55	−	17707.2i	0.0106568	−	0.0672847i
$514$	−232407.	+	319880.i	−0.879675	+	1.21077i
$515$	363895.	+	117714.i	1.37202	+	0.443825i
$516$	25463.9	−	18500.6i	0.0956367	−	0.0694841i
$517$	−265027.	+	135038.i	−0.991538	+	0.505214i
$518$	−90252.1	+	90252.1i	−0.336355	+	0.336355i
$519$	−338281.	−	109914.i	−1.25587	−	0.408055i
$520$	−117268.	+	59943.2i	−0.433682	+	0.221683i
$521$	110593.	+	340369.i	0.407428	+	1.25394i	0.918851	+	0.394606i	$0.129119\pi$
$521$	110593.	+	340369.i	0.407428	+	1.25394i	−0.511422	+	0.859330i	$0.670881\pi$
$522$	−52761.2	+	103550.i	−0.193630	+	0.380021i
$523$	306458.	−	48538.2i	1.12039	−	0.177452i	0.431355	−	0.902182i	$-0.358036\pi$
$523$	306458.	−	48538.2i	1.12039	−	0.177452i	0.689032	+	0.724731i	$0.258036\pi$
$524$			38340.4i			0.139635i
$525$	−226100.	−	309503.i	−0.820316	−	1.12291i
$526$	451855.			1.63315
$527$	1848.52	+	11671.1i	0.00665585	+	0.0420234i
$528$	35251.6	+	17961.6i	0.126448	+	0.0644283i
$529$	−27045.9	+	8787.74i	−0.0966473	+	0.0314026i
$530$	57576.0	−	366607.i	0.204970	−	1.30512i
$531$	29365.9	−	90379.1i	0.104149	−	0.320538i
$532$	32860.9	+	32860.9i	0.116107	+	0.116107i
$533$	−106363.	−	208749.i	−0.374401	−	0.734803i
$534$	−85173.3	−	117231.i	−0.298690	−	0.411112i
$535$	203074.	+	147138.i	0.709490	+	0.514066i
$536$	262039.	+	190382.i	0.912086	+	0.662669i
$537$	−290014.	−	45933.7i	−1.00571	−	0.159288i
$538$	−108877.	+	687425.i	−0.376160	+	2.37498i
$539$	−370766.	+	510316.i	−1.27621	+	1.75656i
$540$	306612.	+	420862.i	1.05148	+	1.44329i
$541$	−395773.	+	287546.i	−1.35223	+	0.982455i	−0.353336	+	0.935496i	$0.614953\pi$
$541$	−395773.	+	287546.i	−1.35223	+	0.982455i	−0.998897	+	0.0469583i	$0.985047\pi$
$542$	459516.	−	234135.i	1.56424	−	0.797018i
$543$	70471.6	−	70471.6i	0.239009	−	0.239009i
$544$	−67639.1	−	21977.3i	−0.228560	−	0.0742637i
$545$	137639.	+	137281.i	0.463392	+	0.462187i
$546$	−94040.1	−	289426.i	−0.315448	−	0.970849i
$547$	76323.1	−	149793.i	0.255083	−	0.500629i	−0.727582	−	0.686021i	$-0.759356\pi$
$547$	76323.1	−	149793.i	0.255083	−	0.500629i	0.982665	+	0.185393i	$0.0593557\pi$
$548$	19151.5	−	3033.30i	0.0637737	−	0.0101008i
$549$			27866.7i			0.0924571i
$550$	−116215.	+	746316.i	−0.384182	+	2.46716i
$551$	−25099.4			−0.0826724
$552$	43741.3	+	276172.i	0.143553	+	0.906361i
$553$	223893.	+	114079.i	0.732134	+	0.373041i
$554$	−115477.	+	37520.6i	−0.376248	+	0.122250i
$555$	−46013.7	−	23369.8i	−0.149383	−	0.0758698i
$556$	−71144.3	+	218960.i	−0.230139	+	0.708296i
$557$	−263184.	−	263184.i	−0.848298	−	0.848298i	0.141623	−	0.989921i	$-0.454768\pi$
$557$	−263184.	−	263184.i	−0.848298	−	0.848298i	−0.989921	+	0.141623i	$0.954768\pi$
$558$	7485.17	+	14690.5i	0.0240399	+	0.0471810i
$559$	6566.18	+	9037.57i	0.0210130	+	0.0289220i
$560$	−50604.1	+	65.8386i	−0.161365	+	0.000209945i
$561$	91622.4	+	66567.6i	0.291123	+	0.211513i
$562$	144993.	+	22964.7i	0.459067	+	0.0727090i
$563$	−12726.2	+	80350.1i	−0.0401497	+	0.253495i	−0.999597	−	0.0283935i	$-0.990961\pi$
$563$	−12726.2	+	80350.1i	−0.0401497	+	0.253495i	0.959447	+	0.281889i	$0.0909609\pi$
$564$	202272.	−	278404.i	0.635884	−	0.875219i
$565$	−514.569	−	395502.i	−0.00161193	−	1.23895i
$566$	598336.	−	434717.i	1.86772	−	1.35698i
$567$	−338223.	+	172333.i	−1.05205	+	0.536048i
$568$	399445.	−	399445.i	1.23811	−	1.23811i
$569$	314179.	+	102083.i	0.970404	+	0.315303i	0.750979	−	0.660326i	$-0.229582\pi$
$569$	314179.	+	102083.i	0.970404	+	0.315303i	0.219425	+	0.975629i	$0.429582\pi$
$570$	−13624.1	+	26825.0i	−0.0419331	+	0.0825637i
$571$	−130154.	−	400574.i	−0.399197	−	1.22860i	−0.925645	−	0.378393i	$-0.876477\pi$
$571$	−130154.	−	400574.i	−0.399197	−	1.22860i	0.526448	−	0.850207i	$-0.323523\pi$
$572$	−170037.	+	333716.i	−0.519698	+	1.01997i
$573$	−55723.6	+	8825.75i	−0.169719	+	0.0268808i
$574$		−	1.53344e6i		−	4.65417i
$575$	−278849.	+	142996.i	−0.843399	+	0.432501i
$576$	−106138.			−0.319908
$577$	23849.5	+	150580.i	0.0716353	+	0.452287i	0.997268	+	0.0738648i	$0.0235333\pi$
$577$	23849.5	+	150580.i	0.0716353	+	0.452287i	−0.925633	+	0.378422i	$0.876467\pi$
$578$	−452187.	−	230401.i	−1.35351	−	0.689649i
$579$	427535.	−	138914.i	1.27531	−	0.414372i
$580$	514808.	−	516149.i	1.53035	−	1.53433i
$581$	−90626.4	+	278919.i	−0.268474	+	0.826279i
$582$	99077.8	+	99077.8i	0.292503	+	0.292503i
$583$	−191104.	−	375063.i	−0.562254	−	1.10349i
$584$	−4454.09	−	6130.52i	−0.0130597	−	0.0179751i
$585$	−24958.6	+	18183.1i	−0.0729302	+	0.0531320i
$586$	−405726.	−	294777.i	−1.18151	−	0.858418i
$587$	−647947.	−	102625.i	−1.88046	−	0.297835i	−0.892319	−	0.451405i	$-0.850923\pi$
$587$	−647947.	−	102625.i	−1.88046	−	0.297835i	−0.988138	+	0.153570i	$0.950923\pi$
$588$	114162.	−	720791.i	0.330193	−	2.08475i
$589$	−2093.00	+	2880.77i	−0.00603308	+	0.00830382i
$590$	−560002.	+	772889.i	−1.60874	+	2.22031i
$591$	285041.	−	207095.i	0.816080	−	0.592917i
$592$	−6070.94	+	3093.30i	−0.0173226	+	0.00882629i
$593$	−416210.	+	416210.i	−1.18359	+	1.18359i	−0.204787	+	0.978807i	$0.565650\pi$
$593$	−416210.	+	416210.i	−1.18359	+	1.18359i	−0.978807	+	0.204787i	$0.934350\pi$
$594$	899416.	+	292238.i	2.54910	+	0.828254i
$595$	−143101.	−	22474.1i	−0.404210	−	0.0634816i
$596$	152985.	+	470841.i	0.430683	+	1.32551i
$597$	18541.7	−	36390.2i	0.0520237	−	0.102102i
$598$	−245746.	+	38922.3i	−0.687201	+	0.108842i
$599$		−	495277.i		−	1.38037i	−0.723634	−	0.690184i	$-0.757530\pi$
$599$		−	495277.i		−	1.38037i	0.723634	−	0.690184i	$-0.242470\pi$
$600$	−108567.	−	331201.i	−0.301576	−	0.920002i
$601$	178818.			0.495066			0.247533	−	0.968879i	$-0.420380\pi$
$601$	178818.			0.495066			0.247533	+	0.968879i	$0.420380\pi$
$602$	11437.9	+	72216.3i	0.0315613	+	0.199270i
$603$	67666.8	+	34478.0i	0.186098	+	0.0948215i
$604$	291765.	−	94800.2i	0.799759	−	0.259858i
$605$	223356.	+	436954.i	0.610220	+	1.19378i
$606$	−55791.8	+	171710.i	−0.151924	+	0.467573i
$607$	−259044.	−	259044.i	−0.703066	−	0.703066i	0.262001	−	0.965068i	$-0.415618\pi$
$607$	−259044.	−	259044.i	−0.703066	−	0.703066i	−0.965068	+	0.262001i	$0.915618\pi$
$608$	−9729.64	−	19095.5i	−0.0263202	−	0.0516564i
$609$	394921.	+	543562.i	1.06482	+	1.46560i
$610$	86141.4	−	266294.i	0.231501	−	0.715653i
$611$	98810.4	+	71789.9i	0.264679	+	0.192301i
$612$	32476.4	+	5143.75i	0.0867091	+	0.0137334i
$613$	14354.9	−	90633.2i	0.0382014	−	0.241194i	−0.961198	−	0.275861i	$-0.911037\pi$
$613$	14354.9	−	90633.2i	0.0382014	−	0.241194i	0.999399	+	0.0346671i	$0.0110371\pi$
$614$	−172980.	+	238087.i	−0.458839	+	0.631538i
$615$	589433.	−	192367.i	1.55842	−	0.508604i
$616$	−791036.	+	574722.i	−2.08466	+	1.51459i
$617$	364200.	−	185569.i	0.956686	−	0.487456i	0.0953232	−	0.995446i	$-0.469612\pi$
$617$	364200.	−	185569.i	0.956686	−	0.487456i	0.861363	+	0.507991i	$0.169612\pi$
$618$	−568251.	+	568251.i	−1.48786	+	1.48786i
$619$	−262162.	−	85181.7i	−0.684209	−	0.222313i	−0.0537721	−	0.998553i	$-0.517124\pi$
$619$	−262162.	−	85181.7i	−0.684209	−	0.222313i	−0.630437	+	0.776240i	$0.717124\pi$
$620$	−16311.7	−	102128.i	−0.0424341	−	0.265681i
$621$	121249.	+	373165.i	0.314408	+	0.967648i
$622$	−50100.9	+	98328.5i	−0.129498	+	0.254155i
$623$	207647.	−	32888.0i	0.534994	−	0.0847347i
$624$		−	16245.5i		−	0.0417219i
$625$	314823.	−	231245.i	0.805947	−	0.591988i
$626$	−1.12676e6			−2.87529
$627$	5338.69	+	33707.2i	0.0135800	+	0.0857407i
$628$	607826.	+	309703.i	1.54120	+	0.785282i
$629$	−18549.3	+	6027.03i	−0.0468841	+	0.0152336i
$630$	−199583.	+	31877.1i	−0.502856	+	0.0803153i
$631$	−23697.6	+	72933.7i	−0.0595177	+	0.183177i	−0.976395	−	0.215992i	$-0.930701\pi$
$631$	−23697.6	+	72933.7i	−0.0595177	+	0.183177i	0.916877	+	0.399169i	$0.130701\pi$
$632$	161573.	+	161573.i	0.404515	+	0.404515i
$633$	126819.	+	248897.i	0.316503	+	0.621172i
$634$	334466.	+	460354.i	0.832097	+	1.14528i
$635$	47769.1	+	146370.i	0.118468	+	0.362998i
$636$	393993.	+	286253.i	0.974034	+	0.707677i
$637$	255821.	+	40518.1i	0.630461	+	0.0998552i
$638$	207119.	−	1.30770e6i	0.508836	−	3.21267i
$639$	77853.4	−	107156.i	0.190667	−	0.262431i
$640$	658232.	+	212926.i	1.60701	+	0.519839i
$641$	573141.	−	416411.i	1.39491	−	1.01346i	0.399600	−	0.916690i	$-0.369149\pi$
$641$	573141.	−	416411.i	1.39491	−	1.01346i	0.995307	−	0.0967691i	$-0.0308508\pi$
$642$	−469500.	+	239222.i	−1.13911	+	0.580406i
$643$	233035.	−	233035.i	0.563636	−	0.563636i	−0.366702	−	0.930338i	$-0.619513\pi$
$643$	233035.	−	233035.i	0.563636	−	0.563636i	0.930338	+	0.366702i	$0.119513\pi$
$644$	−967308.	−	314297.i	−2.33235	−	0.757825i
$645$	−26324.2	+	13456.0i	−0.0632754	+	0.0323442i
$646$	3513.62	+	10813.8i	0.00841958	+	0.0259128i
$647$	−133396.	+	261803.i	−0.318664	+	0.625413i	−0.993662	−	0.112406i	$-0.964144\pi$
$647$	−133396.	+	261803.i	−0.318664	+	0.625413i	0.674999	+	0.737819i	$0.264144\pi$
$648$	−340931.	+	53998.2i	−0.811926	+	0.128596i
$649$			1.08263e6i			2.57035i
$650$	294712.	−	96606.3i	0.697544	−	0.228654i
$651$	95318.8			0.224914
$652$	−82916.6	−	523515.i	−0.195050	−	1.23150i
$653$	−375220.	−	191184.i	−0.879954	−	0.448359i	−0.0451973	−	0.998978i	$-0.514392\pi$
$653$	−375220.	−	191184.i	−0.879954	−	0.448359i	−0.834757	+	0.550619i	$0.814392\pi$
$654$	−388478.	+	126224.i	−0.908262	+	0.295112i
$655$	5587.30	−	35576.3i	0.0130232	−	0.0829237i
$656$	25295.9	−	77852.9i	0.0587818	−	0.180912i
$657$	−1256.35	−	1256.35i	−0.00291059	−	0.00291059i
$658$	362922.	+	712274.i	0.838226	+	1.64511i
$659$	−164991.	−	227090.i	−0.379917	−	0.522911i	0.575646	−	0.817699i	$-0.304751\pi$
$659$	−164991.	−	227090.i	−0.379917	−	0.522911i	−0.955563	+	0.294788i	$0.904751\pi$
$660$	−802661.	−	581573.i	−1.84266	−	1.33511i
$661$	−561772.	−	408151.i	−1.28575	−	0.934153i	−0.286041	−	0.958218i	$-0.592339\pi$
$661$	−561772.	−	408151.i	−1.28575	−	0.934153i	−0.999710	+	0.0240648i	$0.992339\pi$
$662$	1.21111e6	+	191821.i	2.76355	+	0.437703i
$663$	7274.64	−	45930.3i	0.0165495	−	0.104489i
$664$	−156753.	+	215752.i	−0.355532	+	0.489348i
$665$	−25703.1	−	35280.7i	−0.0581223	−	0.0797800i
$666$	−22016.1	+	15995.7i	−0.0496355	+	0.0360623i
$667$	489450.	−	249387.i	1.10016	−	0.560560i
$668$	−435577.	+	435577.i	−0.976141	+	0.976141i
$669$	−429464.	−	139541.i	−0.959565	−	0.311782i
$670$	−540047.	−	538644.i	−1.20305	−	1.19992i
$671$	−98103.9	−	301933.i	−0.217892	−	0.670603i
$672$	−260450.	+	511162.i	−0.576748	+	1.13193i
$673$	−454752.	+	72025.6i	−1.00402	+	0.159022i	−0.636733	−	0.771084i	$-0.719715\pi$
$673$	−454752.	+	72025.6i	−1.00402	+	0.159022i	−0.367291	+	0.930106i	$0.619715\pi$
$674$			1.02456e6i			2.25537i
$675$	−223175.	−	435203.i	−0.489823	−	0.955179i
$676$	−606391.			−1.32697
$677$	1442.65	+	9108.53i	0.00314763	+	0.0198733i	0.989212	−	0.146490i	$-0.0467976\pi$
$677$	1442.65	+	9108.53i	0.00314763	+	0.0198733i	−0.986065	+	0.166363i	$0.946798\pi$
$678$	740455.	+	377281.i	1.61079	+	0.820740i
$679$	−193338.	+	62819.4i	−0.419351	+	0.136256i
$680$	−117442.	−	59647.5i	−0.253984	−	0.128995i
$681$	74627.8	−	229681.i	0.160919	−	0.495257i
$682$	−132819.	−	132819.i	−0.285555	−	0.285555i
$683$	−49538.8	−	97225.4i	−0.106195	−	0.208419i	0.831794	−	0.555084i	$-0.187314\pi$
$683$	−49538.8	−	97225.4i	−0.106195	−	0.208419i	−0.937989	+	0.346665i	$0.887314\pi$
$684$	5824.04	+	8016.11i	0.0124484	+	0.0171337i
$685$	−18212.8	+	23.6959i	−0.0388147	+	5.05000e-5i
$686$	405083.	+	294310.i	0.860788	+	0.625399i
$687$	93744.5	+	14847.7i	0.198624	+	0.0314590i
$688$	−610.591	+	3855.12i	−0.00128995	+	0.00814444i
$689$	−101596.	+	139835.i	−0.214012	+	0.294563i
$690$	−856.699	−	658466.i	−0.00179941	−	1.38304i
$691$	−258066.	+	187496.i	−0.540473	+	0.392677i	−0.824261	−	0.566210i	$-0.808409\pi$
$691$	−258066.	+	187496.i	−0.540473	+	0.392677i	0.283787	+	0.958887i	$0.408409\pi$
$692$	1.04828e6	−	534123.i	2.18909	−	1.11540i
$693$	−162110.	+	162110.i	−0.337555	+	0.337555i
$694$	−784242.	−	254816.i	−1.62829	−	0.529063i
$695$	97924.0	−	192806.i	0.202731	−	0.399165i
$696$	188798.	+	581061.i	0.389744	+	1.19951i
$697$	106380.	−	208783.i	0.218976	−	0.429764i
$698$	−20314.1	+	3217.44i	−0.0416952	+	0.00660388i
$699$		−	103422.i		−	0.211669i
$700$	1.25271e6	+	195070.i	2.55655	+	0.398101i
$701$	836920.			1.70313			0.851565	−	0.524249i	$-0.175654\pi$
$701$	836920.			1.70313			0.851565	+	0.524249i	$0.175654\pi$
$702$	−60746.6	−	383539.i	−0.123267	−	0.778279i
$703$	−5236.73	−	2668.25i	−0.0105962	−	0.00539903i
$704$	1.14999e6	−	373655.i	2.32033	−	0.753921i
$705$	−228261.	+	228856.i	−0.459255	+	0.460452i
$706$	−78275.4	+	240907.i	−0.157042	+	0.483326i
$707$	−185222.	−	185222.i	−0.370556	−	0.370556i
$708$	−568637.	−	1.11601e6i	−1.13441	−	2.22640i
$709$	100835.	+	138788.i	0.200595	+	0.276096i	0.897450	−	0.441117i	$-0.145418\pi$
$709$	100835.	+	138788.i	0.200595	+	0.276096i	−0.696854	+	0.717213i	$0.745418\pi$
$710$	−1.07521e6	+	783325.i	−2.13293	+	1.55391i
$711$	43344.0	+	31491.2i	0.0857412	+	0.0622946i
$712$	188820.	+	29906.2i	0.372468	+	0.0589931i
$713$	12191.2	−	76972.2i	0.0239810	−	0.151410i
$714$	178904.	−	246240.i	0.350932	−	0.483016i
$715$	206411.	−	284878.i	0.403757	−	0.557247i
$716$	785742.	−	570875.i	1.53269	−	1.11356i
$717$	762254.	−	388388.i	1.48273	−	0.755488i
$718$	48393.2	−	48393.2i	0.0938719	−	0.0938719i
$719$	938092.	+	304805.i	1.81463	+	0.589609i	0.999953	+	0.00969192i	$0.00308508\pi$
$719$	938092.	+	304805.i	1.81463	+	0.589609i	0.814676	+	0.579917i	$0.196915\pi$
$720$	−10658.7	−	1673.97i	−0.0205608	−	0.00322910i
$721$	−360294.	−	1.10887e6i	−0.693086	−	2.13310i
$722$	384676.	−	754970.i	0.737940	−	1.44829i
$723$	−260466.	+	41253.7i	−0.498281	+	0.0789200i
$724$			329649.i			0.628890i
$725$	−552912.	+	403916.i	−1.05191	+	0.768450i
$726$	−1.03113e6			−1.95631
$727$	158548.	+	1.00103e6i	0.299979	+	1.89399i	0.430571	+	0.902557i	$0.358312\pi$
$727$	158548.	+	1.00103e6i	0.299979	+	1.89399i	−0.130592	+	0.991436i	$0.541688\pi$
$728$	357730.	+	182272.i	0.674982	+	0.343921i
$729$	−562063.	+	182625.i	−1.05762	+	0.343642i
$730$	8122.11	+	15889.4i	0.0152413	+	0.0298168i
$731$	−3452.60	+	10626.0i	−0.00646118	+	0.0198855i
$732$	259715.	+	259715.i	0.484702	+	0.484702i
$733$	351074.	+	689021.i	0.653417	+	1.28240i	0.945379	+	0.325973i	$0.105692\pi$
$733$	351074.	+	689021.i	0.653417	+	1.28240i	−0.291962	+	0.956430i	$0.594308\pi$
$734$	688438.	+	947554.i	1.27783	+	1.75878i
$735$	−210972.	+	652191.i	−0.390526	+	1.20726i
$736$	379464.	+	275697.i	0.700512	+	0.508952i
$737$	−854543.	−	135346.i	−1.57325	−	0.249179i
$738$	51145.7	−	322921.i	0.0939067	−	0.592903i
$739$	364136.	−	501190.i	0.666768	−	0.917728i	−0.332913	−	0.942957i	$-0.608032\pi$
$739$	364136.	−	501190.i	0.666768	−	0.917728i	0.999682	+	0.0252295i	$0.00803166\pi$
$740$	162280.	−	52961.4i	0.296347	−	0.0967154i
$741$	11336.9	−	8236.76i	0.0206471	−	0.0150010i
$742$	−1.00800e6	+	513602.i	−1.83085	+	0.932865i
$743$	−252913.	+	252913.i	−0.458136	+	0.458136i	−0.898043	−	0.439907i	$-0.855011\pi$
$743$	−252913.	+	252913.i	−0.458136	+	0.458136i	0.439907	+	0.898043i	$0.355011\pi$
$744$	82434.4	+	26784.6i	0.148923	+	0.0483881i
$745$	−73341.2	−	459191.i	−0.132140	−	0.827334i
$746$	−11682.3	−	35954.3i	−0.0209918	−	0.0646061i
$747$	−28387.7	+	55714.0i	−0.0508732	+	0.0998443i
$748$	−369987.	+	58600.2i	−0.661277	+	0.104736i
$749$		−	764495.i		−	1.36273i
$750$	131562.	+	810171.i	0.233888	+	1.44030i
$751$	−89028.4			−0.157852			−0.0789258	−	0.996880i	$-0.525149\pi$
$751$	−89028.4			−0.157852			−0.0789258	+	0.996880i	$0.525149\pi$
$752$	6675.77	+	42149.2i	0.0118050	+	0.0745338i
$753$	−361368.	−	184126.i	−0.637323	−	0.324732i
$754$	−517045.	+	167998.i	−0.909465	+	0.295503i
$755$	−284546.	+	45447.2i	−0.499181	+	0.0797285i
$756$	490528.	−	1.50969e6i	0.858263	−	2.64146i
$757$	434876.	+	434876.i	0.758881	+	0.758881i	0.976119	−	0.217238i	$-0.0697048\pi$
$757$	434876.	+	434876.i	0.758881	+	0.758881i	−0.217238	+	0.976119i	$0.569705\pi$
$758$	−468393.	−	919273.i	−0.815215	−	1.59995i
$759$	−439020.	−	604259.i	−0.762080	−	1.04891i
$760$	−12314.9	−	37734.3i	−0.0213209	−	0.0653295i
$761$	30717.7	+	22317.7i	0.0530419	+	0.0385372i	0.613990	−	0.789314i	$-0.289563\pi$
$761$	30717.7	+	22317.7i	0.0530419	+	0.0385372i	−0.560948	+	0.827851i	$0.689563\pi$
$762$	−319535.	−	50609.3i	−0.550311	−	0.0871606i
$763$	92707.0	−	585329.i	0.159244	−	1.00543i
$764$	109688.	−	150973.i	0.187920	−	0.258650i
$765$	−29385.5	−	9505.67i	−0.0502122	−	0.0162428i
$766$	−329496.	+	239393.i	−0.561555	+	0.407994i
$767$	396093.	−	201819.i	0.673296	−	0.343062i
$768$	−433237.	+	433237.i	−0.734520	+	0.734520i
$769$	−955079.	−	310324.i	−1.61505	−	0.524762i	−0.644285	−	0.764786i	$-0.722845\pi$
$769$	−955079.	−	310324.i	−1.61505	−	0.524762i	−0.970767	+	0.240023i	$0.922845\pi$
$770$	2.05025e6	−	1.04802e6i	3.45800	−	1.76761i
$771$	150608.	+	463523.i	0.253360	+	0.779762i
$772$	−675048.	+	1.32486e6i	−1.13266	+	2.22297i
$773$	1.03550e6	−	164008.i	1.73298	−	0.274477i	0.791407	−	0.611290i	$-0.209349\pi$
$773$	1.03550e6	−	164008.i	1.73298	−	0.274477i	0.941571	+	0.336813i	$0.109349\pi$
$774$			15589.3i			0.0260222i
$775$	252.774	+	97142.0i	0.000420852	+	0.161735i
$776$	−184857.			−0.306981
$777$	24611.6	+	155391.i	0.0407659	+	0.257386i
$778$	772528.	+	393623.i	1.27631	+	0.650311i
$779$	67155.1	−	21820.0i	0.110663	−	0.0359567i
$780$	−63146.6	+	402077.i	−0.103791	+	0.660876i
$781$	−466295.	+	1.43511e6i	−0.764466	+	2.35278i
$782$	−175963.	−	175963.i	−0.287745	−	0.287745i
$783$	389222.	+	763891.i	0.634854	+	1.24597i
$784$	53193.7	+	73214.8i	0.0865422	+	0.119115i
$785$	−518873.	−	375953.i	−0.842019	−	0.610090i
$786$	61217.9	+	44477.4i	0.0990907	+	0.0719936i
$787$	−543918.	−	86148.1i	−0.878181	−	0.139090i	−0.298965	−	0.954264i	$-0.596641\pi$
$787$	−543918.	−	86148.1i	−0.878181	−	0.139090i	−0.579216	+	0.815174i	$0.696641\pi$
$788$	−182308.	+	1.15105e6i	−0.293598	+	1.85370i
$789$	327380.	−	450600.i	0.525894	−	0.723831i
$790$	−316850.	−	434916.i	−0.507691	−	0.696869i
$791$	−975428.	+	708690.i	−1.55899	+	1.13267i
$792$	−185751.	+	94644.7i	−0.296128	+	0.150885i
$793$	−92177.4	+	92177.4i	−0.146581	+	0.146581i
$794$	−867743.	−	281947.i	−1.37642	−	0.447225i
$795$	−323874.	−	323032.i	−0.512438	−	0.511106i
$796$	41745.4	+	128479.i	0.0658843	+	0.202771i
$797$	−342689.	+	672566.i	−0.539491	+	1.05881i	0.446930	+	0.894569i	$0.352517\pi$
$797$	−342689.	+	672566.i	−0.539491	+	1.05881i	−0.986420	+	0.164241i	$0.947483\pi$
$798$	90589.7	−	14348.0i	0.142257	−	0.0225313i
$799$			122156.i			0.191347i
$800$	−521630.	−	264076.i	−0.815047	−	0.412619i
$801$	44824.5			0.0698635
$802$	−310208.	−	1.95858e6i	−0.482286	−	3.04503i
$803$	18035.5	+	9189.52i	0.0279702	+	0.0142515i
$804$	951981.	−	309317.i	1.47271	−	0.478511i
$805$	851770.	+	432603.i	1.31441	+	0.667572i
$806$	−23833.7	+	73352.6i	−0.0366878	+	0.112913i
$807$	606631.	+	606631.i	0.931489	+	0.931489i
$808$	−108138.	−	212233.i	−0.165636	−	0.325080i
$809$	596069.	+	820418.i	0.910751	+	1.25354i	0.966910	+	0.255119i	$0.0821146\pi$
$809$	596069.	+	820418.i	0.910751	+	1.25354i	−0.0561592	+	0.998422i	$0.517885\pi$
$810$	812870.	−	1057.59i	1.23894	−	0.00161193i
$811$	−429534.	−	312075.i	−0.653064	−	0.474479i	0.211249	−	0.977432i	$-0.432247\pi$
$811$	−429534.	−	312075.i	−0.653064	−	0.474479i	−0.864314	+	0.502953i	$0.832247\pi$
$812$	−2.19500e6	−	347654.i	−3.32907	−	0.527272i
$813$	99446.0	−	627877.i	0.150455	−	0.949935i
$814$	182231.	−	250819.i	0.275025	−	0.378540i
$815$	647.737	+	497856.i	0.000975177	+	0.749529i
$816$	13145.0	−	9550.41i	0.0197415	−	0.0143431i
$817$	−2999.88	+	1528.51i	−0.00449427	+	0.00228995i
$818$	1.24738e6	−	1.24738e6i	1.86420	−	1.86420i
$819$	89529.8	+	29090.0i	0.133475	+	0.0433686i
$820$	−928691.	+	1.82854e6i	−1.38116	+	2.71942i
$821$	254765.	+	784087.i	0.377967	+	1.16326i	0.941455	+	0.337139i	$0.109459\pi$
$821$	254765.	+	784087.i	0.377967	+	1.16326i	−0.563488	+	0.826124i	$0.690541\pi$
$822$	17373.7	−	34097.9i	0.0257128	−	0.0504643i
$823$	22801.7	−	3611.44i	0.0336642	−	0.00533189i	−0.139580	−	0.990211i	$-0.544575\pi$
$823$	22801.7	−	3611.44i	0.0336642	−	0.00533189i	0.173244	+	0.984879i	$0.444575\pi$
$824$		−	1.06023e6i		−	1.56151i
$825$	660043.	+	656617.i	0.969760	+	0.964726i
$826$	2.90963e6			4.26459
$827$	16244.7	+	102565.i	0.0237520	+	0.149964i	0.996714	−	0.0810009i	$-0.0258117\pi$
$827$	16244.7	+	102565.i	0.0237520	+	0.149964i	−0.972962	+	0.230965i	$0.925812\pi$
$828$	−193219.	−	98450.0i	−0.281831	−	0.143600i
$829$	621412.	−	201909.i	0.904213	−	0.293797i	0.180238	−	0.983623i	$-0.442313\pi$
$829$	621412.	−	201909.i	0.904213	−	0.293797i	0.723975	+	0.689826i	$0.242313\pi$
$830$	443497.	−	444652.i	0.643775	−	0.645452i
$831$	−46249.3	+	142341.i	−0.0669735	+	0.206123i
$832$	−351083.	−	351083.i	−0.507181	−	0.507181i
$833$	117607.	+	230817.i	0.169490	+	0.332643i
$834$	267079.	+	367603.i	0.383980	+	0.528503i
$835$	467652.	−	340699.i	0.670733	−	0.488650i
$836$	−91323.5	−	66350.4i	−0.130668	−	0.0949361i
$837$	120132.	+	19027.0i	0.171477	+	0.0271593i
$838$	−41496.5	+	261998.i	−0.0590913	+	0.373088i
$839$	535382.	−	736891.i	0.760572	−	1.04684i	−0.236595	−	0.971608i	$-0.576031\pi$
$839$	535382.	−	736891.i	0.760572	−	1.04684i	0.997166	−	0.0752287i	$-0.0239687\pi$
$840$	−623422.	+	860418.i	−0.883534	+	1.21941i
$841$	398846.	−	289779.i	0.563915	−	0.409708i
$842$	−1.76951e6	+	901612.i	−2.49591	+	1.27173i
$843$	127952.	−	127952.i	0.180050	−	0.180050i
$844$	−878755.	−	285525.i	−1.23362	−	0.400829i
$845$	562675.	+	88368.7i	0.788032	+	0.123761i
$846$	52669.5	+	162100.i	0.0735900	+	0.226487i
$847$	679169.	−	1.33294e6i	0.946697	−	1.85800i
$848$	−59648.9	+	9447.46i	−0.0829489	+	0.0131378i
$849$		−	911638.i		−	1.26476i
$850$	251424.	+	181673.i	0.347992	+	0.251450i
$851$	128630.			0.177617
$852$	−273098.	−	1.72427e6i	−0.376217	−	2.37534i
$853$	−494389.	−	251904.i	−0.679470	−	0.346207i	0.0799583	−	0.996798i	$-0.474521\pi$
$853$	−494389.	−	251904.i	−0.679470	−	0.346207i	−0.759428	+	0.650591i	$0.774521\pi$
$854$	−811460.	+	263659.i	−1.11263	+	0.361516i
$855$	−4235.99	−	8286.94i	−0.00579460	−	0.0113360i
$856$	214823.	−	661157.i	0.293179	−	0.902313i
$857$	778087.	+	778087.i	1.05942	+	1.05942i	0.998120	+	0.0612957i	$0.0195233\pi$
$857$	778087.	+	778087.i	1.05942	+	1.05942i	0.0612957	+	0.998120i	$0.480477\pi$
$858$	335589.	+	658630.i	0.455861	+	0.894678i
$859$	45738.6	+	62953.8i	0.0619864	+	0.0853169i	0.838885	−	0.544309i	$-0.183208\pi$
$859$	45738.6	+	62953.8i	0.0619864	+	0.0853169i	−0.776898	+	0.629626i	$0.783208\pi$
$860$	30097.1	−	93041.0i	0.0406937	−	0.125799i
$861$	−1.52918e6	−	1.11101e6i	−2.06278	−	1.49869i
$862$	764661.	+	121110.i	1.02909	+	0.162992i
$863$	−159599.	+	1.00767e6i	−0.214293	+	1.35299i	0.612492	+	0.790477i	$0.290167\pi$
$863$	−159599.	+	1.00767e6i	−0.214293	+	1.35299i	−0.826785	+	0.562518i	$0.809833\pi$
$864$	−430284.	+	592236.i	−0.576405	+	0.793354i
$865$	−1.05054e6	+	342853.i	−1.40404	+	0.458221i
$866$	53835.2	−	39113.5i	0.0717844	−	0.0521544i
$867$	−557382.	+	284000.i	−0.741506	+	0.377816i
$868$	−222939.	+	222939.i	−0.295901	+	0.295901i
$869$	−580492.	−	188613.i	−0.768700	−	0.249766i
$870$	−226921.	−	1.42076e6i	−0.299804	−	1.87708i
$871$	109782.	+	337875.i	0.144709	+	0.445368i
$872$	244653.	−	480159.i	0.321749	−	0.631469i
$873$	−42809.7	+	6780.39i	−0.0561712	+	0.00889664i
$874$		−	74988.5i		−	0.0981684i
$875$	−1.13397e6	−	363562.i	−1.48110	−	0.474857i
$876$	−23418.2			−0.0305173
$877$	−60526.3	−	382148.i	−0.0786946	−	0.496858i	−0.995282	−	0.0970239i	$-0.969068\pi$
$877$	−60526.3	−	382148.i	−0.0786946	−	0.496858i	0.916587	−	0.399834i	$-0.130932\pi$
$878$	−292121.	−	148843.i	−0.378943	−	0.193081i
$879$	−587918.	+	191026.i	−0.760920	+	0.247238i
$880$	121380.	−	19386.6i	0.156740	−	0.0250343i
$881$	212515.	−	654055.i	0.273803	−	0.842680i	−0.715730	−	0.698377i	$-0.753906\pi$
$881$	212515.	−	654055.i	0.273803	−	0.842680i	0.989534	−	0.144303i	$-0.0460940\pi$
$882$	255584.	+	255584.i	0.328547	+	0.328547i
$883$	−638105.	−	1.25235e6i	−0.818410	−	1.60622i	−0.795090	−	0.606492i	$-0.792576\pi$
$883$	−638105.	−	1.25235e6i	−0.818410	−	1.60622i	−0.0233199	−	0.999728i	$-0.507424\pi$
$884$	90410.9	+	124440.i	0.115695	+	0.159241i
$885$	365007.	+	1.11842e6i	0.466031	+	1.42797i
$886$	1.31746e6	+	957187.i	1.67830	+	1.21935i
$887$	1.08075e6	+	171174.i	1.37366	+	0.217566i	0.799247	−	0.601002i	$-0.205232\pi$
$887$	1.08075e6	+	171174.i	1.37366	+	0.217566i	0.574410	+	0.818568i	$0.305232\pi$
$888$	−22380.2	+	141303.i	−0.0283816	+	0.179195i
$889$	275890.	−	379730.i	0.349086	−	0.480476i
$890$	−428344.	−	138562.i	−0.540770	−	0.174929i
$891$	745952.	−	541965.i	0.939626	−	0.682679i
$892$	1.33084e6	−	678094.i	1.67261	−	0.852237i
$893$	−26029.1	+	26029.1i	−0.0326404	+	0.0326404i
$894$	929262.	+	301935.i	1.16269	+	0.377780i
$895$	−812288.	+	415214.i	−1.01406	+	0.518353i
$896$	−651719.	−	2.00578e6i	−0.811791	−	2.49844i
$897$	−139235.	+	273264.i	−0.173046	+	0.339623i
$898$	−297983.	+	47195.8i	−0.369520	+	0.0585263i
$899$		−	170283.i		−	0.210693i
$900$	257298.	+	82861.5i	0.317651	+	0.102298i
$901$	−172874.			−0.212951
$902$	582678.	+	3.67888e6i	0.716169	+	4.52171i
$903$	80302.9	+	40916.4i	0.0984817	+	0.0501789i
$904$	−1.04272e6	+	338800.i	−1.27594	+	0.414579i
$905$	48039.4	−	305884.i	0.0586544	−	0.373473i
$906$	187100.	−	575834.i	0.227938	−	0.701521i
$907$	197648.	+	197648.i	0.240258	+	0.240258i	0.816957	−	0.576699i	$-0.195659\pi$
$907$	197648.	+	197648.i	0.240258	+	0.240258i	−0.576699	+	0.816957i	$0.695659\pi$
$908$	362650.	+	711741.i	0.439862	+	0.863278i
$909$	−32827.5	−	45183.2i	−0.0397292	−	0.0546826i
$910$	−765626.	−	554739.i	−0.924557	−	0.669894i
$911$	−682787.	−	496074.i	−0.822713	−	0.597736i	0.0947751	−	0.995499i	$-0.469787\pi$
$911$	−682787.	−	496074.i	−0.822713	−	0.597736i	−0.917488	+	0.397762i	$0.869787\pi$
$912$	4835.95	+	765.939i	0.00581423	+	0.000920883i
$913$	111438.	−	703595.i	0.133688	−	0.844075i
$914$	−547601.	+	753708.i	−0.655498	+	0.902216i
$915$	−203143.	−	278839.i	−0.242639	−	0.333052i
$916$	−253984.	+	184530.i	−0.302702	+	0.219926i
$917$	−97818.5	+	49841.0i	−0.116328	+	0.0592718i
$918$	274628.	−	274628.i	0.325881	−	0.325881i
$919$	1.24423e6	+	404276.i	1.47323	+	0.478682i	0.932083	−	0.362245i	$-0.117990\pi$
$919$	1.24423e6	+	404276.i	1.47323	+	0.478682i	0.541149	+	0.840927i	$0.317990\pi$
$920$	615073.	+	613475.i	0.726693	+	0.724805i
$921$	112097.	+	345000.i	0.132153	+	0.406724i
$922$	365495.	−	717325.i	0.429952	−	0.843828i
$923$	611974.	−	96927.2i	0.718339	−	0.113774i
$924$			3.02171e6i			3.53923i
$925$	−158298.	+	25494.4i	−0.185009	+	0.0297963i
$926$	−1.07623e6			−1.25511
$927$	−38888.3	−	245531.i	−0.0452542	−	0.285724i
$928$	913168.	+	465282.i	1.06036	+	0.540282i
$929$	415025.	−	134850.i	0.480886	−	0.156249i	−0.0585351	−	0.998285i	$-0.518643\pi$
$929$	415025.	−	134850.i	0.480886	−	0.156249i	0.539422	+	0.842036i	$0.318643\pi$
$930$	−181989.	−	92430.1i	−0.210416	−	0.106868i
$931$	−24122.8	+	74242.4i	−0.0278310	+	0.0856550i
$932$	241891.	+	241891.i	0.278476	+	0.278476i
$933$	61756.2	+	121203.i	0.0709442	+	0.139236i
$934$	−1.34458e6	−	1.85065e6i	−1.54132	−	2.12144i
$935$	351853.	−	457.780i	0.402475	−	0.000523641i
$936$	69253.6	+	50315.7i	0.0790480	+	0.0574317i
$937$	−295391.	−	46785.3i	−0.336448	−	0.0532881i	−0.0140750	−	0.999901i	$-0.504480\pi$
$937$	−295391.	−	46785.3i	−0.336448	−	0.0532881i	−0.322373	+	0.946613i	$0.604480\pi$
$938$	−363750.	+	2.29663e6i	−0.413426	+	2.61027i
$939$	−816364.	+	1.12363e6i	−0.925876	+	1.27436i
$940$	−1391.01	−	1.06914e6i	−0.00157425	−	1.20998i
$941$	722673.	−	525053.i	0.816136	−	0.592958i	−0.0994670	−	0.995041i	$-0.531714\pi$
$941$	722673.	−	525053.i	0.816136	−	0.592958i	0.915603	+	0.402083i	$0.131714\pi$
$942$	1.19962e6	−	611236.i	1.35189	−	0.688822i
$943$	−1.09275e6	+	1.09275e6i	−1.22885	+	1.22885i
$944$	147722.	+	47997.9i	0.165769	+	0.0538615i
$945$	−675170.	+	1.32937e6i	−0.756048	+	1.48861i
$946$	−54881.7	−	168909.i	−0.0613261	−	0.188742i
$947$	−154481.	+	303186.i	−0.172256	+	0.338072i	−0.960953	−	0.276710i	$-0.910756\pi$
$947$	−154481.	+	303186.i	−0.172256	+	0.338072i	0.788697	+	0.614782i	$0.210756\pi$
$948$	697458.	−	110466.i	0.776070	−	0.122917i
$949$		−	8311.54i		−	0.00922888i
$950$	14862.7	+	92284.5i	0.0164683	+	0.102254i
$951$	701405.			0.775546
$952$	62816.9	+	396610.i	0.0693111	+	0.437613i
$953$	−337423.	−	171926.i	−0.371526	−	0.189302i	0.258251	−	0.966078i	$-0.416854\pi$
$953$	−337423.	−	171926.i	−0.371526	−	0.189302i	−0.629777	+	0.776776i	$0.716854\pi$
$954$	−229402.	+	74537.2i	−0.252058	+	0.0818986i
$955$	−123782.	+	124104.i	−0.135722	+	0.136076i
$956$	−874428.	+	2.69121e6i	−0.956772	+	2.94464i
$957$	−1.15400e6	−	1.15400e6i	−1.26004	−	1.26004i
$958$	−148088.	−	290638.i	−0.161357	−	0.316681i
$959$	32635.1	+	44918.4i	0.0354852	+	0.0488413i
$960$	1.06204e6	−	773727.i	1.15238	−	0.839547i
$961$	727600.	+	528632.i	0.787854	+	0.572410i
$962$	−125735.	−	19914.5i	−0.135865	−	0.0215189i
$963$	25498.7	−	160992.i	0.0274957	−	0.173601i
$964$	512711.	−	705686.i	0.551720	−	0.759377i
$965$	819451.	−	1.13097e6i	0.879971	−	1.21450i
$966$	−1.62398e6	+	1.17989e6i	−1.74031	+	1.26441i
$967$	−336255.	+	171331.i	−0.359597	+	0.183224i	−0.624450	−	0.781065i	$-0.714677\pi$
$967$	−336255.	+	171331.i	−0.359597	+	0.183224i	0.264853	+	0.964289i	$0.414677\pi$
$968$	961922.	−	961922.i	1.02657	−	1.02657i
$969$	13329.5	+	4331.02i	0.0141960	+	0.00461257i
$970$	430050.	+	67539.8i	0.457062	+	0.0717821i
$971$	−382096.	−	1.17597e6i	−0.405260	−	1.24726i	−0.920678	−	0.390324i	$-0.872363\pi$
$971$	−382096.	−	1.17597e6i	−0.405260	−	1.24726i	0.515417	−	0.856939i	$-0.327637\pi$
$972$	281631.	−	552732.i	0.298090	−	0.585035i
$973$	−651121.	+	103127.i	−0.687758	+	0.108930i
$974$			113364.i			0.119497i
$975$	117188.	−	363888.i	0.123275	−	0.382788i
$976$	−45547.4			−0.0478150
$977$	−206039.	−	1.30088e6i	−0.215854	−	1.36285i	−0.822902	−	0.568183i	$-0.807647\pi$
$977$	−206039.	−	1.30088e6i	−0.215854	−	1.36285i	0.607049	−	0.794665i	$-0.292353\pi$
$978$	−932081.	−	474919.i	−0.974487	−	0.496526i
$979$	−485670.	+	157804.i	−0.506729	+	0.164646i
$980$	−1.03196e6	−	2.01883e6i	−1.07451	−	2.10208i
$981$	39045.7	−	120170.i	0.0405728	−	0.124870i
$982$	−1.53733e6	−	1.53733e6i	−1.59420	−	1.59420i
$983$	−215243.	−	422438.i	−0.222752	−	0.437175i	0.752402	−	0.658704i	$-0.228895\pi$
$983$	−215243.	−	422438.i	−0.222752	−	0.437175i	−0.975154	+	0.221529i	$0.928895\pi$
$984$	−1.01028e6	−	1.39054e6i	−1.04340	−	1.43612i
$985$	336905.	−	1.04150e6i	0.347244	−	1.07346i
$986$	−439896.	−	319603.i	−0.452477	−	0.328744i
$987$	973243.	+	154146.i	0.999049	+	0.158234i
$988$	−7250.92	+	45780.5i	−0.00742812	+	0.0468993i
$989$	43311.6	−	59613.3i	0.0442804	−	0.0609468i
$990$	466710.	−	152315.i	0.476186	−	0.155407i
$991$	−661667.	+	480729.i	−0.673739	+	0.489500i	−0.871275	−	0.490795i	$-0.836706\pi$
$991$	−661667.	+	480729.i	−0.673739	+	0.489500i	0.197535	+	0.980296i	$0.436706\pi$
$992$	129550.	−	66009.0i	0.131648	−	0.0670780i
$993$	1.06877e6	−	1.06877e6i	1.08389	−	1.08389i
$994$	3.85692e6	+	1.25319e6i	3.90363	+	1.26837i
$995$	−20012.7	−	125300.i	−0.0202144	−	0.126563i
$996$	254679.	+	783821.i	0.256728	+	0.790129i
$997$	−283470.	+	556342.i	−0.285179	+	0.559695i	−0.988508	−	0.151169i	$-0.951696\pi$
$997$	−283470.	+	556342.i	−0.285179	+	0.559695i	0.703329	+	0.710865i	$0.251696\pi$
$998$	−1.15523e6	+	182970.i	−1.15986	+	0.183705i
$999$			200755.i			0.201157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.12.9	✓	72
5.2	odd	4		125.5.f.a.43.1		72
5.3	odd	4		125.5.f.b.43.9		72
5.4	even	2		125.5.f.c.82.1		72
25.2	odd	20		125.5.f.c.93.1		72
25.11	even	5		125.5.f.b.32.9		72
25.14	even	10		125.5.f.a.32.1		72
25.23	odd	20	inner	25.5.f.a.23.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.12.9	✓	72	1.1	even	1	trivial
25.5.f.a.23.9	yes	72	25.23	odd	20	inner
125.5.f.a.32.1		72	25.14	even	10
125.5.f.a.43.1		72	5.2	odd	4
125.5.f.b.32.9		72	25.11	even	5
125.5.f.b.43.9		72	5.3	odd	4
125.5.f.c.82.1		72	5.4	even	2
125.5.f.c.93.1		72	25.2	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02122 + 6.44773i) q^{2} +(7.16973 + 3.65316i) q^{3} +(-25.3134 + 8.22483i) q^{4} +(24.6871 - 3.94298i) q^{5} +(-16.2327 + 49.9591i) q^{6} +(-53.8906 - 53.8906i) q^{7} +(-31.4629 - 61.7494i) q^{8} +(-9.55120 - 13.1461i) q^{9} +O(q^{10})\)	\(q+(1.02122 + 6.44773i) q^{2} +(7.16973 + 3.65316i) q^{3} +(-25.3134 + 8.22483i) q^{4} +(24.6871 - 3.94298i) q^{5} +(-16.2327 + 49.9591i) q^{6} +(-53.8906 - 53.8906i) q^{7} +(-31.4629 - 61.7494i) q^{8} +(-9.55120 - 13.1461i) q^{9} +(50.6343 + 155.149i) q^{10} +(149.767 + 108.812i) q^{11} +(-211.537 - 33.5042i) q^{12} +(11.8912 - 75.0782i) q^{13} +(292.438 - 402.506i) q^{14} +(191.404 + 61.9158i) q^{15} +(21.4870 - 15.6112i) q^{16} +(67.7399 - 34.5152i) q^{17} +(75.0086 - 75.0086i) q^{18} +(21.7886 + 7.07953i) q^{19} +(-592.485 + 302.858i) q^{20} +(-189.510 - 583.252i) q^{21} +(-548.646 + 1076.78i) q^{22} +(-495.228 + 78.4364i) q^{23} -557.665i q^{24} +(593.906 - 194.682i) q^{25} +496.227 q^{26} +(-122.417 - 772.910i) q^{27} +(1807.40 + 920.915i) q^{28} +(-1041.95 + 338.551i) q^{29} +(-203.750 + 1297.35i) q^{30} +(-48.0298 + 147.821i) q^{31} +(-661.474 - 661.474i) q^{32} +(676.280 + 1327.28i) q^{33} +(291.722 + 401.521i) q^{34} +(-1542.89 - 1117.91i) q^{35} +(349.898 + 254.216i) q^{36} +(-253.383 - 40.1319i) q^{37} +(-23.3960 + 147.717i) q^{38} +(359.529 - 494.849i) q^{39} +(-1020.20 - 1400.36i) q^{40} +(2493.49 - 1811.63i) q^{41} +(3567.12 - 1817.54i) q^{42} +(-103.917 + 103.917i) q^{43} +(-4686.07 - 1522.60i) q^{44} +(-287.626 - 286.879i) q^{45} +(-1011.47 - 3113.00i) q^{46} +(-729.454 + 1431.63i) q^{47} +(211.086 - 33.4327i) q^{48} +3407.40i q^{49} +(1861.76 + 3630.53i) q^{50} +611.766 q^{51} +(316.498 + 1998.29i) q^{52} +(-2026.03 - 1032.31i) q^{53} +(4858.50 - 1578.62i) q^{54} +(4126.36 + 2095.73i) q^{55} +(-1632.16 + 5023.27i) q^{56} +(130.355 + 130.355i) q^{57} +(-3246.95 - 6372.49i) q^{58} +(3437.49 + 4731.30i) q^{59} +(-5354.34 + 6.96628i) q^{60} +(-1387.41 - 1008.01i) q^{61} +(-1002.16 - 158.726i) q^{62} +(-193.731 + 1223.17i) q^{63} +(3839.28 - 5284.31i) q^{64} +(-2.47245 - 1900.35i) q^{65} +(-7867.28 + 5715.91i) q^{66} +(-4164.25 + 2121.79i) q^{67} +(-1430.85 + 1430.85i) q^{68} +(-3837.19 - 1246.78i) q^{69} +(5632.37 - 11089.8i) q^{70} +(2518.85 + 7752.22i) q^{71} +(-511.256 + 1003.40i) q^{72} +(107.996 - 17.1049i) q^{73} -1674.73i q^{74} +(4969.34 + 773.817i) q^{75} -609.771 q^{76} +(-2207.09 - 13935.0i) q^{77} +(3557.81 + 1812.80i) q^{78} +(-3135.73 + 1018.86i) q^{79} +(468.897 - 470.118i) q^{80} +(1539.14 - 4736.97i) q^{81} +(14227.3 + 14227.3i) q^{82} +(-1746.99 - 3428.67i) q^{83} +(9594.30 + 13205.4i) q^{84} +(1536.21 - 1119.18i) q^{85} +(-776.148 - 563.905i) q^{86} +(-8707.30 - 1379.10i) q^{87} +(2006.98 - 12671.6i) q^{88} +(-1621.42 + 2231.69i) q^{89} +(1555.99 - 2147.50i) q^{90} +(-4686.83 + 3405.18i) q^{91} +(11890.8 - 6058.66i) q^{92} +(-884.373 + 884.373i) q^{93} +(-9975.72 - 3241.31i) q^{94} +(565.811 + 88.8612i) q^{95} +(-2326.12 - 7159.06i) q^{96} +(1210.96 - 2376.64i) q^{97} +(-21970.0 + 3479.71i) q^{98} -3008.14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

Modular forms

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